That's basically what happened to the characters Fredrick Kato, Joan Croce, and Scott Riley. Though like I've said it might get too cramped in there. If you want to maybe do something with @Snagglepuss89's character separately, maybe they were in a squad and are sleeping in a different barracks room?
You're probably fine to hop in, although it might get cramped in the barracks. You might want to hold off until the second trials begins, unless you want to do things that are independent from the current parties?