The one thing your son (or any athlete for that matter) absolutely has to do to get better at his sport is... to practice his sport.
So while I'm not necessarily advocating for or against fall ball I just think it is helpful to keep this in mind.
Your son needs time to develop -- not as a weightlifter or as a sprinter -- but as a pitcher. I'm not saying that lifting, running, etc. shouldn't be a part of his strength & conditioning program. (They should!) I'm just saying that, at some point, these are not sufficient to make him a better pitcher.
When I was in college, I fell prey to the mentality that all I needed to do was get bigger, stronger, faster and somehow that would translate into more success on the mound.
I was right. (Up to a certain point.)
And then I was very, very wrong.
What I actually needed was to transition back to practicing my sport; honing my craft; deliberate practice, as Daniel Coyle puts it in his book, "The Talent Code". (Which I highly recommend if you haven't read it yet.)
And the only way to do that was to get on the mound and pitch.
So, having said all that, I think it might be helpful for you to consider the following:
Is fall ball the most constructive environment available for my son to develop as a pitcher?
Hope that helps!