When your children first joined the team were they invited or did you inquire about it?
Our gym is invite as well but I know you can ask for an evaluation. I would see that as most useful if you are moving to a new gym and they do not know your child. Usually, the coaches are watching the recreation classes for potential gymnasts and if your child has "it" they ask you to join and there is nothing more you need to do. I know some gyms use the open tryout method but that seems to be less used.
My only caution would be, if you ask for an evaluation, this "could" set the child up for a face-to-face dissapointment. Just be sure the child has the personality to be okay with that. Also, I know that they watch physical skills but they also tend to look for a type of mentality. Kids who are self motivated or who look like they are so happy jumping around like they just can't stop, the ability to follow careful directions, are a few early signs of kids that would do well on team. Skills can be taught, personality can't. I hope that makes sense!