Hello manni3. I'm not a grammar expert, of course (I come from the translating side of the business), so I could easily be wrong, but these are my thoughts:
1) Function: What is the word "great" modifying? An adverb modifies a verb, adjective, adverb, prepositional phrase, or sentence, doesn't it? Is that what "great" is doing? I don't think so.
2) Form: "Great" does not have a separate adverbial form, so let's use an adjective that does: "It's not so random a problem." We wouldn't say "It's not so randomly a problem." Therefore not an adverb.
So far I'm saying no, it's not adverbial, and this is apparently the view reflected in Langenscheidts Kurzgrammatik (see #9), however...
3) Gut feeling, for which I have no explanation :-(
Despite (1) and (2), the phrase "not so great a" does have a kind of adverbial feel about it. I have no idea why. Maybe someone else does (hope).