Edit: Please read this later answer which corrects much of the mistakes that the Japanese sources (that I used) have with more recent and accurate Chinese information. I'll keep this answer around so that it can be seen what was actually corrected.
Short answer:
While the relevant set of strokes in 壌 is indeed a version of 衣, the lower set of strokes in 展 should not be considered as such. Thus, IMO you should not use them interchangeably.
Long Version:
Before we start: I am no scholar of this subject, just an enthusiast that did some research for this answer, so read this more as an informed opinion rather than the ultimate answer. Especially, when it comes to 漢字 there might be differences depending on the person you are asking. Furthermore, I am basing myself mostly on internet resources. They might well be wrong, or the conclusions I am making might be wrong, but I thought I might as well just share the insights I have gotten from my little research.
Classifying 漢字 by their parts
Now, as has been pointed out in a previous answer you have to differentiate between the 部首 (radicals) and auxiliary parts of the 漢字. The character 衣 you are referring to, when appearing in other characters, is referred to as ころもへん. And you can consult in this and this list that characters containing ころもへん as 部首 will always have the ''complete'' character in it. I.e. the one not ''missing'' any strokes.
In particular, you will notice that 展 is not part of that list (as pointed out by the previous answer, since the radical is 尸).
Now you might ask yourself, why does it look so similar and what is its relation to other 漢字 with the same parts such as 長 or 喪. And I think it's worth to take a little time to differentiate things that don't belong together.
As you might have guessed by the chapter title or the last paragraph, there are ways to classify 漢字 by the parts they are using and what function they have for the character. I think, the most popular one is [六書]{りくしょ}. It contains the following distinctions (of which there is a nice readup on here):
- [象形]{しょうけい} - characters that originate from the looks of what they mean (i.e. hieroglyphs), e.g. how 水 looks a bit like flowing water.
- [指事]{しじ} - characters which represent an abstract idea, e.g. 三 which represents the concept of the number three by three lines.
- [会意]{かいい} - combination of multiple meaningful parts, e.g. 男 which has 田 for (rice) field and 力 for power and suggests the imagery of a strong man working in the fields.
- [形声]{けいせい} - combination of meaningful and purely phonetic characters, e.g. [晴]{せい} which means clear skies and is made up of 日 for sun indicating good weather and [青]{せい} for it's reading. 85% of japanese characters are made up like this (source), which is why you can usually try to guess reading based on the contained parts.
- [転注]{てんちゅう} - apply extended meaning to a character, e.g. 楽 comes from 音楽 for music, but since listening to music is pleasant it has also become used in as one way of writing [楽]{たの}しい, which means something like fun or pleasant.
- [仮借]{かしゃく} - borrowing characters with similar sound to convey a certain term (more known under the name of [当]{あ}て[字]{じ}), e.g. writing アジア (Asia) as 亜細亜 completely ignoring the original meaning.
Note that the latter two are more about usage (使用法) of characters than their construction (構成法). Now that the vocabulary is down, let us get to some examples.
Examples
I feel the need to first cover 長 and 喪 to emphasize that the bottom part is not just a sloppily written ころもへん. Then I will quickly go over 壌. And lastly 展, which will be the most ambiguous section since there seems to have been a shift in its classification.
Disclaimer
All images below are from okjiten a great source for this kind of material and it gives a great read, albeit I do not know it's sources so read with that in mind. Another great resource is the 説文解字 database which gives you access to the book of the same name, which is the oldest source that splits the 漢字 into their respective radicals. It is written during the late han-dynasty by a certain [許慎]{きょしん} who was a Chinese that settled over to Japan apparently. I do think that okjiten bases itself on this. But I can't read Chinese so I can't confirm the information.
長

The characters meaning is long. As the image depicts, 長 is a 象形文字 (class 1 character). It originally depicted a person with long hair and transformed into the character it is today. No relation at all to 衣.
喪

The characters meaning is usually something along the lines of mourning. As the image depicts in old writing there was a dog with upright ears (象形文字 class 1), two mouths (象形文字 class 1) and a corpse at the bottom (象形文字 class 1). This is a prime example of a 会意文字 (class 3 character). You have the dog with the two mouths (nowadays 哭 for wailing). The wailing dog is used to convey the image of wailing people at the sight of the dead person. So it is using the meaning of all the sub-parts. Again no direct link to 衣.
壌

As you can probably guess from the use cases of this kanji (mostly connected to soil) this is a 形声文字 (class 4 character) which retains it's meaning of soil 土 and borrows the reading from [襄]{じょう}. For what it's worth, the image is still explaining that originally this character is made up of symbols depicting the stashing away of some dirt amulet in your clothes to protect you from evil, and this is why one has the 衣 and thus the correct writing of it, since it was an integral part to the meaning of the character.
展

According to the figure above the interpretation is that there is a corpse (尸) with its arms and legs outstretched (象形文字 class 1). The 㠭 below it is imagery for heavy weight (象形文字 class 1) and finally the bottom part is an old form of clothes or at least some parts of them (the collar to translate exactly) on which all this weight is placed. The character is figuratively depicting the placing of weight onto clothes to stretch them wide (伸ばし広げる). This meaning of stretching is still retained in the character today albeit not in connection with clothes. You might notice that the concept of clothes itself is not as prevalent as in the previous character (which might be the reason it is not contained nowadays). The character can be found in 説文解字 here.
Now this is where it becomes weird. If we take a look at this question dealing with exactly your problem with this character there are citations from dictionaries from way back that read like the following
尸(からだ)と、音符●テン(×・△はその省略形。ころがる意→転)とから成り、人がからだをころがして寝返りをうつ意……
などという説明があります。
この「音符●」の「●」は、何やら漢字になっていない記号のようなもの(象形文字?)で、「△」は「展」の「尸」を除いた部分、「×」は「展」の「尸」を除いた部分と少し形の異なる字(?)です。
To give a quick summary (the characters from the dictionary could not be copied over, since they are not actual japanese characters, so placeholders ●,×,△ have been inserted). The dictionary explains that this is a pure 形声文字 (class 4 character) in which the meaning is largely conveyed through [尸]{からだ} and the part inside it is just [音符]{おんぷ}, i.e. the phonetic addendum to give a way to read the character. So no relation at all to ころもへん which is also what Chocolate commented on the question with his findings in his 漢和辞典.
But okjiten has connected the character with the meaning of collar and thus somehow to 衣 and thus classifies it not only as a 形声文字 (class 4 character) but claims that the middle part also plays a part in the meaning (which it does, if you follow their reasoning) and thus classifies it as [会意形声文字]{かいいけいせいもじ}, which is a combination of class 3 and class 4. This means that the (previously believed to be purely) phonetic part actually carries some of the original meaning of the character. As the link explains it was added because most of the time characters classified purely as
形声文字 (class 4 characters) actually could also be classified as 会意文字 (class 3 character), as well.
To sum the story up for this character, there doesn't seem to be a consensus. And I can most certainly not tell you whether the dictionaries are old or whether the internet is taking some artistic liberties (some native/scholar opinion would be needed). Though I would personally tend towards the former. Which does not change the fact that the collar of clothes part mutated into something which is the bottom part of the unrelated 喪 and has grown completely unrelated, in meaning and writing, to 衣.
Conclusion
I hope this has shed a bit of light onto this very niche topic for you. I wonder if anybody kept themselves motivated to read until this point over the question of one little line that most people probably don't even actively notice. In any case, I hope my point is clear. While the characters might be similar, they are not the same. It seems that this particular stroke order just naturally evolved from a plethora of different base characters, rather than being based on one single characters like radicals usually are.
While there does seem to be the occasional historical reference to 衣, it is probably better to consider it non-existent if it is not the exact ころもへん in the kanji. It might hint at the fact that the meaning probably evolved, or the relation to 衣 was not strong enough to begin with, to keep that ころもへん in the character.
While it is nice to take a look into history like this, a good baseline is not to diverge from what you learned and keep to consensus.