My gymmie is about the same age as OP's. Coach will usually come out and tell me at pickup time about minor mishaps if she thinks there will be any lasting soreness or complaints from my daughter. For example: "Just so you know, she kind of rolled her ankle landing a jump. She said it hurt so we iced it and she sat out tumble track, but now you can see she is running around just fine and playing hide and seek with the other girls. If she starts limping later on, that's why." Another day it was: "There is a big red patch on her arm where she hit the beam when she fell. Nothing seemed broken or sprained, so I told her I was impressed that she got right back up on the beam." I don't think notification of these little bumps and bruises is strictly necessary, but I do appreciate getting a more objective perspective on the situation than what I may hear from my daughter later. I also like how Coach uses these opportunities to explain to my daughter the difference between being really injured (which means you stop and tell Coach immediately) and just getting a little banged up, which is a normal part of gymnastics.
On the other hand, I would definitely want to know about any potential injury involving the head or neck, even if the coach didn't see it or think it was serious. Something like, "Your daughter told me that she fell into the pit and her neck hurt. I didn't see it and she didn't show any signs of injury at the time, but I just thought you should know." That way, if the kid starts feeling or acting unusual later on, the parent knows to consider the possibility of a concussion.