If it's a legitimate question, it shouldn't matter who asked it. Don't worry about who's asking the question, judge the question on its own merits.
As such, if the post isn't spam, I say it shouldn't be flagged as spam. If it's a good question, it probably shouldn't be downvoted (Of course, your votes are yours to do with as you will). As others have stated, however, flagging the post for moderator attention to let them know that the troll is circumventing post bans is perfectly legitimate. I just don't believe that a good post from a bad user should suffer for the actions of the asker.
I've dealt with many of this user's accounts, and tried to figure out a way to handle them, so I can explain my approach so far. First, I should comment that this user has been an ongoing nuisance since the start of the year, and we've probably deleted something like 100+ of their accounts since then. They've worked around IP bans and other extreme measures to continue to post here, and have posted some rather odd content. I seriously think this is a person who needs real psychological help, from other things I've found out there by them.
They generally follow a pattern of posting decent or borderline questions for a little bit, then flipping out and posting diatribes about the FBI or a Google robots.txt conspiracy (among the more tame things they've posted). Because they aren't here to contribute positively, and show no signs of improving, I typically delete their accounts on sight.
However, I leave any good questions alone. I do not destroy their accounts (which automatically removes everything posted by a user) and instead simply delete them. Unfortunately, even the latter has the consequence of triggering a deletion of downvoted content by that user, so sometimes acceptable but downvoted questions get removed at that point.
In general, judging a question only on its own merits, as StephenTG answered, seems the right thing to do.
An argument against that, though, would be for extreme cases of a troll playing a long game and posting good questions in order to ultimately cause more damage.
Someone with a set of good questions could decide to use the power of their ownership of those questions to delete them (temporarily damaging SE, at least until someone restores them), or to maliciously alter them so that their answers no longer match (causing confusion and damaged SE while it is figured out).
Not judging the user is probably the best policy, and sticking to it might be good just for consistency, but we should keep in mind what could be done by a troll owning a set of good questions (or answers). Their questions might end up being more trouble than they are worth.