This might be a weird question, but does Openbound save your progress as you go? I've never really played any of the flash games in Homestuck, but since I know Openbound is a really long one, I'll have to leave my computer at some point, so if I reload the page, will the game start where I left off?

Unfortunately no, it has to be done in one go. But Openbound is three different flash games so you can take breaks inbetween them.