If you are a successful bullet player, then it is because you can quickly see tactics, and you quickly recognize tactics that are used against you and stop them. It is almost instantaneous. If you can see those in bullet, you won't miss them in normal games.
Just the opposite... what you miss in bullet, you'll probably see in longer games. Bullet, when it comes down to it, is about time, not about tactics. When I play Blitz, if Ican force my opponent to stop and think for a while, I robbed him of time he may need later, so often unsound moves work quite well - but that doesn't make them good moves they might even be losing moves, but trying to prove them losing without adequate time can often prove impossible.
"Do you think you'd have more tactical repition from playing one 2-hour game, or 120 1-minute games?"
No. You get tactical training from studying tactices, playing through anotated master games and from deeply studying positions and learning the themes. Playing fast does none of that because you're too busy... umm.. playing fast.
Yes, but it is the slow chess that gives you the tactical patterns to make you good at the bullet chess; not the other way around.
Tactics cause bullet to improve, but it doesn't necessarily follow that the converse is true, that bullet causes tactics to improve. I have argued that the converse is in fact not true, for reasons given in my previous posts.