If you live breed a stallion, it changes their behavior - for good, whether they are gelded or not. Sure, there is the one in a million that doesn't change, but that's one in a million, and probably not a more active breed like a Thoroughbred.
That would be the biggest issue, really. A 'stallion that does not know he is a stallion' behaves very, very differently from one that has been used for live breeding.
You have to think about whether that is really worth it. You will, by all odds, have 'a stallion that knows he is a stallion' all of a sudden, and that carries certain disadvantages - it affects how the horse behaves both at a show and at home, how he can be stabled, turned out, etc.
Unless you are very used to dealing very effectively with the absolute worst possible behavior, I'd say no.
Why 'used to dealing effectively with the absolute worst possible behavior'? Because there is no guarantee that it won't happen, or even, that what a stud manager would call 'a little studdy' is to you something horrific that gets you or anyone else hurt.
I'd geld him now and breed her to a stallion that is selected because he is a good match for her bloodlines and conformation, not one that just happened to show up at my barn.