Yes, its perfectly normal and I'm sure she would love the outing.
This is between the young man in question and his mom. If he wants her to be there, perhaps waiting in the waiting room, and she doesn't mind waiting, then it's okay with me, if it's okay with them. When my son turned 12 and went to get a school physical, I went with him for all the initial questions and the height and weight check. Then I went to the waiting room, as we agreed to in advance, to wait for him to be done.
This is between mom and son and what works for them.