I believe the original poster was ambiguous about the player being male or female, but the question is valid for both, although the answer may vary as I believe on the girls side it is very common for prep players to roster and play on club teams at nationals.
In fact, most of the older players on the CT Polar Bears do that as well as the players on Assabet Valley (the top female organization in MA).
My D had the opportunity to play club with her old team in addition to her prep school this season. However, we passed due to family financial issues. It wouldn't have been a weekly game on Sundays, but a 4 weekend/holiday tournament situation to qualify for nationals.
If things look better next year, she may very well be playing there again.
I can't speak to the boys side, but I am not familiar with any boys prep players who also roster on club teams.
Hey commish, can you move this thread to the Prep School forum?
Been there, done that. Went somewhere else and did it again.