FAA (and the airlines that bother to ask you about your medical status) aren't too concerned with a VA disability per se, they are more interested in the specific details of the issue(s) in question.

TBI, PTSD, and any mental issues will be subject to much higher scrutiny than something like a rotator cuff. I suspect TBI would be no-go in many or most cases.

If you have multiple issues for the VA, maybe be selective about what you claim disability for? I wouldn't hide anything in your military record from the FAA (they have cross-checked other federal records in the recent past) but claiming something with the VA tends emphasize that particular issue.