Nah. The initial pool of members is determined once you enter the room for the first time. It is possible to load a save before that to have the pool re-rolled, and you can repeat this process when the chapters change and you get those two additional people, but on the latter case it only affects the new guys. Once determined, the pool is not re-rolled no matter how many times you exit and enter.
Overall, I find that stuff very anal as you will eventually get everyone anyway and the real star players become so only later on.
okay, remembered it wrong.