Tournament viablity, as strange as this sounds, is not determined by tournament results. Its dictated by matchups and obviously matchups occur in tournaments so bear with me. If everyone was playing the game and not playing MK he'd be unviable in tournaments by that other defintion. If a character can win, or hold their own (meaning they have a feasible chance of winning) in a significant portion of thier matchups with other characters used in tournaments then they can be considered tournament viable. As far as what exactly that "significant portion" is, I won't pretend and make up an arbitrary number of matchups but I would dare say around half or more. DK is still viable for this reason even though D3 counters him so badly. We've already discussed in detail why tournament results aren't irrevocable proof of character quality.
But talking about a character being tournament viable is ultimately going to be inconclusive since you have weird characters that can suck against characters placed 8-3 and have great matchups with the top 1 and 2 and all kinds of weird stuff like that. Once people figure out the matchups we won't need the tier list. Tournament viable is really a bad term since Azen can be tournament viable with anyone. Falcon won't ever be considered tournament viable though.
As far as the ICs go I'm not sure what exactly your asking but yes technically they don't fit the model for Brawl. However, they aren't top/high tier. They're wierd like that yes in that they can punish but they don't really since they still have lower tier attributes like bad range, priority, bad approaches, less access to their good moves, and so on. Sure they can punish, but their grab range and the other stipulations that require them to infinite limit them severely. So with the exception of the punishment thing they meet the opposite of the criteria of what I outlined for a good character. Naturally, that would be the criteria for a bad character.
Uh what does Falcon have going for him. Someone was saying he's not bad but I really disagree. He really has bad approaches especially in the air. You could argue that he's got Down or Side B but if your opponent plays like most people in Brawl do they'll shield both attacks especially Side B since it has so much startup lag. Down B has alot of post lag so I'd hardly call them safe. All his smashes are slow as well as his tilts which lack prioriy and have either pre or post lag. I'd challenge anyone to find 3 good things about him that I can't find a considerable downside to. As I've said before Brawl is Moves over Movement and he doesn't have good moves. This also factors into why Sonic will never be a great character. He may go up but I doubt it'll be significant.