In this sentence, bad is modifying the verb draw (and yes, modify is the word you want there). Consider these examples:
Slash draws bad(ly).
I draw bad(ly).
I draw as bad(ly) as Slash.
Sometimes it's hard to figure out clauses and phrases with as or so because they can be so vague and ambiguous, but in this case it is indeed modifying the verb. And as such, it should have the -ly ending of adverbs (but only if you're concerned about being formally correct—in colloquial speech and writing, it's almost never a big deal).
