I already have Lvl. 3 Gym, and Lvl. 3 Training Court infrastructure along with all Lvl.1 Health&Recovery Center, TV&Radio Station, and Merchandise Store.
Having a Gym helps your trainee have a slight boost in skill training. As for the Training Court infrastructure, it helps your whole team work on their free throw shooting without actually setting the said skill in your weekly training.
So, yeah, I think it's worth investing to when you have a trainee. And that 700k of yours, use it to expand your arena. I suggest expanding bleachers first, it's the cheapest yet profitable.