If the workouts are unofficial how are they a problem? Problem for the basketball coach or problem with the high school section?
My son used to borrow the batting cage key during lunch while still playing basketball and lifted weights with the football team before school. Not sure if he was breaking any rules in CA but the AD/basketball coach didn't seem bothered by it.
btw, if he is a position player, a lot can be done with just a tee and net. i.e. hit into net and throw into net.
I'm sure if varies by state. In CA my understanding is that an athlete can play "club" sport and associated activity while on playing another "in season" sport, but if the other team is a school activity, even if unofficial, it's not allowed. In any case, the unofficial baseball workouts going on right now take place at the same time as varsity baskeball practice so it's a moot point in our case.
Even if there wasn't a conflict, I'm not sure that lifting and going to basketball practice afterwards would be a great idea. You need time to recover. And to do homework!