I'm sure that there will be obnoxious Bills fans, if this were ever to happen.
That being said, we will be nothing like the Patriots* fans. The reason why? The vast majority of these "fans" are all a bunch of phonies.
They are not fans of the team, they're Tom Brady fans. The fakest fanbase around.
Believe me, I've met them. They have no clue about any of their history. They don't know who Stanley Morgan, John Hannah, Irving Fryar, Steve Grogan, Andre Tippett & Fred Marion are. Trust me, they are old enough to know who those players are.
Hell, they probably don't know who Ben Coates is and that Pete Carroll was once their head coach. Nor that for the longest time the Patriots home jersey was red.
Bills fans will probably be obnoxious after winning a championship, but at least they will know all there is to know about the team(s) they cheer for.