In general, is it allowed to bind the scroll wheel to another button in a PC game?

Yes, it's actually recommended in a lot of speedgames to allow for faster, repetitive actions. Portal is a notable example of this, where you bind it to jump. Make sure you ask the moderators of your game though.

Every game/category has its own rules about this sort of thing, so always check the rules/with the moderators for whatever game(s) you're planning on running.

For an example of when this is not allowed, you can't rebind the scroll wheel to change weapon in Cuphead. So you should always ask, as shiken said