I can't remember exactly, but I lost one guy and the crew got liquified. I'd done all the loyalty quests and got all the upgrades.

Thinking back, I seem to recall discovering that there's apparently a chance of losing one guy no matter what, all you can do is minimize it.

Also, I did a lot of sidequests after unlocking the route to the final mission. Apparently the game does notice your delay, as that determines whether you have a crew at the end or some nutrient-rich soup.