If you missed the official tryouts and they have open spots, having him join the team for some workouts is logical. I've certainly seen the opposite scenario, pre-tryouts, having a kid the coach is potentially interested in coming and skating with the team to assess fit, ability, etc. And a conversation follows that would indicate if they should officially tryout, or seek another situation. Not sure there is a "typical" in this situation as it isn't formalized like a tryout period, but if the coach and organization are halfway decent they realize the more time you spend with them, the less time you have to find another team if this isn't going to work out. So, I would ask the question, but believe a decision can be made after a couple interactions at most.
Are you paying for the time with the team? Or you an invited guest?