Can I play Halo: Reach with bad internet?

Ehh, it might be one of those things where you can, but you might get kicked from the game for bad connection. If you do have a bad connection I recommend that you don't. Because Halo: Reach has an Auto-ban system, where it bans players from the multilayer if they quit matches early. A stupid idea from Bungie.

There's no way to tell exactly how well it will work. Ethernet cables (I assume you use for desktop) are a lot faster than Wi-Fi. The only thing I know for sure is that the shared data plan and most data plans are good for phones and maybe tablets. Computers and gaming where you play online and watch videos will run through 2gb of data insanely quickly. In the past 2 months my laptop alone not even including my Xbox 360, Xbox One, Phone, and Ipad, has used 260gb of data.

So internet can only be determined by comparing it to what else you have and trying it yourself. The only way you can tell if something is going to be faster/slower is by knowing computer specs. If you try to run Halo on a really bad computer, it will have an awful frame rate no matter how good or bad your internet is.