So, the situation I was worried about came to pass. I submitted the game late Friday night, got three hours of sleep, and went to work on Saturday morning. While at work my gamejame teammates start sending me messages about how they keep getting softlocked by a glitch. So I had to race home, hunt down the bug, fix it, and upload an updated version of the game with like 45 minutes left before the deadline.
If we couldn't update our submissions, I would have submitted an unplayable game! I didn't think I'd have any time to fix anything after work today, but the stars aligned and friends came through.