So, I want to participate in this for at least the first two days, but my internet connection is kind of awful.

Would it be okay if I do this Jam in a 24 period ahead of time (Sunday perhaps) and then upload it ASAP the day of to be sure nothing goes wrong, or do I need to specifically do it on the day? (Obviously this isn't possible for day 2, but would it be okay for day 1)

I think that would be okay, if you didn't add to the game on the day you submit it. Say, for instance, you want to participate on day one. You would be able to submit it that day, as long as you worked on it within the same time limit as you normally would, instead of working on it an extra day, just work on it the day before, but submit the file without changing it on submission day. please forgive my Ingrish.

Basically, you can, if you don't spend extra time than normal on the game, and you submit it on the correct date(and not too late!). I would certainly let that slip, this is just meant to reduce the time you are working on any given project, but if you are creating the project within the same time-span, then it still was created with the same level of difficulty, so there isn't much of a difference!