My son has a very similiar situation. He will be working out with the football team and the baseball team this winter. The good thing is the strength and conditioning coach is the same coach, so he knows to alternate the workouts so he is not doubling up on the same group of muscles.
He had the opprtunity to train outside the school training but he decide to stay with the team for the leadership and team bonding aspect. He is in his junior year and is going to be counted on as a team leader.
He felt that he could not lead the team if he did not sweat with the team.
However I do agree that as long as you show improvement and it is evident to the coach that you have been working you should be fine, but I would suggest that you talk to the coach. Communciation is key.