Background: problematic circumstances for understanding
Poetry is a really difficult format for trying to learn any language, precisely because poetry uses different structures and omits various things.
In addition, translation is a terrible way to try to understand the mechanics of any source language, precisely because the process of translation unavoidably results in different grammar and mechanics in the target language.
Looking more closely at the text
In your sample, the 白く is adverbial, applying not to the noun, but rather to the overall line / sentence. Note too that whitespace is not a common feature in written Japanese -- so if someone is adding spaces, it's meant more like punctuation.
Let's break it down, word by word.
[白く]{whitely } [白く]{whitely } [吹雪]{blizzard }[の]{[POSS] }[よう]{likeness }[な]{[MOD] } [そう]{that way }[出逢う]{encounter }[前]{before }[から]{from }[解って]{understanding/knowing }[た]{was } [この]{this }[想い]{thought/feeling }
↑
whitely, whitely, like a blizzard, knowing it from before meeting like that, this feeling
The whitely here isn't necessarily limited in scope to just the blizzard, but instead kind of sets the mood or scenery for the whole line.
Your second line:
[強く]{strongly } [強く]{strongly } [願い]{wish/desire }[は]{[TOPIC] }[強く]{strongly } [繋ぐ]{tie together }[よ]{[EMPH]} [その]{that/those }[手]{hand(s) }[を]{[OBJ]}
↑
strongly, strongly, the wishes/desires (are strong / strongly)*, [I?] tie [them] together! those hands
Here again, the strongly isn't necessarily limited in scope. Also, we have some poetic license, deliberately mixing things to allow for additional allusions and associations.
The asterisk here points out this key phrase. Sometimes an adverbial form is used conjunctively. In teaching materials for English-language readers, we are often taught that the conjunctive ("this and [something else]") form for "-i" adjectives needs to be ~くて, but in reality, folks sometimes use just ~く.
In the line of the poem, this phrase about the "wishes" or "desires" could be interpreted two ways -- as a separate statement using the conjunctive adverbial, wherein the speaker / poet is stating that their "wish/desire" simply is "strong, and...", or mixed into the rest of the line, wherein somehow the "wish/desire" is being strongly tied together with the hands, perhaps alluding to getting married. I suspect that both interpretations are intended, and that the ambiguity is deliberate.
Initial questions
Let's loop back to what you specifically asked.
Is it possible that there just may be a verb that is being implied?
Absolutely, that is possible. As poetry, though, that may have been deliberately omitted. Sometimes too, an adverb is used to establish the "mood" or "scene" for the current context. Consider English adverbial phrases used to start a sentence, such as "like the dawning of the day,..." or even just "surprisedly,..." I suspect that is how the adverbs are being used here.
I'm not sure why it's translated as a comparative adjective
I'm not either. I suspect the translator was taking a few liberties to try to create the target-language text. There's nothing here that implies any comparison, or any change in degree of adjectiveness.
... and if it does mean something like "White, white, like a blizzard," could the phrase have been written as "白い 白い 吹雪のような" instead?
It could, but the meaning does shift in doing so -- the scope of meaning for 白い would be limited to the 吹雪. Again, 白く 白く is not necessarily describing the blizzard, and appears to be coloring the entire scene and context. Even the 想い, implying a blankness or emptiness.
And the second line says "My wishes get stronger", but the "get" part is missing. Could it be that there is actually a になる phrase that is only implied?
No, the translation here is off. There's nothing at all in the source text about getting or becoming stronger. The 強く is describing either 1) the 願い themselves, 2) the manner in which その手 should be 繋ぐ-ed, or 3) both.
Notes
I'd like to comment again that poetry is difficult to interpret even in one's mother tongue, and poetry in translation is, unfortunately, an awful way to try to learn another language. If you're looking at this as a way of understanding the process of translating poetry, this is great exercise! :) If you're trying to understand the Japanese by looking at the translation, I'd recommend avoiding poetry altogether. If you're trying to understand techniques of expression in Japanese by looking at Japanese poetry, that's difficult, but potentially rewarding advanced stuff -- just don't get caught up in the translation. 😄
Please comment if the above does not address your question.