I've never been good at making bets, so should I just give you a dollar or two now to save time?
I don't believe it's probable (or even possible), but the only way I could see CBS saying, "What do we care about the studio, let him have it," is if Peters' production company had to sign legally binding papers that they would not step into the Trek arena in any way in any future project, and that CBS will be very vigilant in seeing that nothing that can even remotely be associated with a piece of CBS IP ever comes out of that studio. In any case, I don't see Axanar ever making it onto film in any form. Both sides don't deserve a win in this case. And if he completely "de-Trekifies" it, then who's to say he can't turn it into a commercial film? No, I don't think any form of Axanar (or any space battle movie) is going to happen.
At the same time, I don't see that because CBS believes its IP was used as a promotion/inducement for funds so Peters could build that studio. Considering the scope of the studio project and its stated future uses, that's a pretty big no-no for CBS overlook. They aren't venture capitalists, after all.