Did つ (助数詞) actually mean の?
No.
Did つ (not as a 助数詞) actually mean の?
Yes, in some ways, sometimes.
Breaking things down
Japanese has several different つ elements that can come at the end of things.
つ〔助動詞〕
Indicates completion of verb action, also known as the perfective aspect. This was much more productive in older stages of the language. It persists in modern Japanese as the て conjunctive ending, in certain set construction patterns like 行き[つ]{●}戻り[つ]{●}, and in the つつ continuative ending as in 変わり[つ]{●}[つ]{●}ある.
The modern past-tense ending た evolved from classical たり, which in turn was a contraction of the 連用形{れんようけい} or continuative form て of this same つ, + あり: て + あり → たり → た.
つ〔副助詞〕
Affixed to terms describing amounts or portions, and indicating that each amount or portion is of equal size. Equivalent to, and possibly derived from, ずつ. That said, ずつ is from older spelling づつ which is listed in some dictionaries as a reduplication of the counter つ (see below).
つ〔接尾／助数詞〕
A counter, suffixed to native-Japanese numbers as a nominalizer (i.e. it forms nouns). In modern Japanese, you generally need a の between [NUMBER]つ and a noun, but in Old Japanese, this could be immediately followed by a noun.
My dead-tree copy of Shogakukan's 国語{こくご}大辞典{だいじてん}, 大辞泉{だいじせん} at Kotobank, and 大辞林{だいじりん} at Kotobank, all list this as the 訓読み for the counter suffix 個 or 箇, more commonly read as ko or ka.
つ〔格助詞〕
This is the one you're thinking of.
Described in Daijirin (third つ entry down) as:
体言または体言に準ずるものに付いて，連体修飾語をつくる。
Attaches to a nominal or a something acting as a nominal, and forms an attributive modifier.
This is like modern uses of の when one noun, or noun-like term or phrase, is used to modify another. 青い車の人 "a blue-car person → a person of the blue car", 犬飼いの人 "a dog-keeping person → a person who is keeping a dog", etc.
It's a fine distinction, but it appears that Old Japanese つ in this particle usage did not indicate possession (one thing belonging to another): that was expressed by either が or の. According to Shogakukan, the distinction between the two was that が indicated a closer relationship than の.
Derivations
If you're interested in the question of where the heck did this all come from, a fellow named Bjarke Frellesvig has been doing some interesting research into the origins of the Japanese language. If memory serves, he has a theory that the ancient precursor to the Japanese language may have had two kinds of copula (like English "is" or "to be"), one that started with n and gave rise to the particles に and の and the perfective ending ぬ, and one that started with t and gave rise to the particles て and と and the perfective ending つ. Many moons ago, snailplane recommended Frellesvig's A History of the Japanese Language, which I have yet to dive into. I suspect this would be a good deep-dive book for the Japanese learner who is also a hardcore word nerd.
Addendum
The final つ in みっつ is the noun-forming counter. According to Shogakukan, the modern 促音{そくおん} (geminate) readings like みっつ、よっつ are just sound shifts from earlier みつ、よつ, and are not evidence of みつ + つ.
We know that these number words are nouns as they can be followed by particles such as は and に and を, in constructions that require nouns or noun phrases. This holds true even back to the Man'yōshū, where we can find instances of ひとつ immediately followed by these particles.
Notably, Japanese does not always require a の between one noun and another, when the first noun is modifying the second one. In the modern language, there are examples of this all over the place -- but these are more commonly thought of as compounds, words like 日本猿{にほんざる} (Japanese macaque) or 雲形{くもがた} (cloud shape) or 兎小屋{うさぎごや} (rabbit hutch). Similarly, 七{なな}つ (seven, the seventh of something) + 時{とき} (hour) = 七{なな}つ時{どき} (the seventh hour in the old timekeeping system).
