I recently completed a mathematics BA and have started 4 year ROTC commitment in the US military. The military has offered to let me get my PhD in Operation Research(OR) while being on Active Duty(full pay and benefits) starting in August. I had planned on becoming an academic after the military and my research interests are in Theory of Computation and Logic. Originally my career plan was getting a PhD in Math(logic or theory of computation), CS(theory of computation) or even Philosophy(logic), but getting in a PhD program right now fully paid for is very tempting. I am interested in OR, but I will eventually focus on Logic or Theory of Computation. If I do not purse an OR graduate degree I will be doing mostly managerial functions for the next four years. I think getting the PhD in OR and doing technical work might be a more efficient use of my 20's, than doing a traditional military leadership. I have noticed some very well respect Professors do not have their PhD in the exact field they are currently doing research.
To my questions:
Would getting a PhD in operational research immediately preclude me from tenure track position in Math, CS and Philosophy Departments? Even if I have a solid amount of publications?
If so, would already having a PhD hurt me if I applied for admission to a PhD program in Math, CS or philosophy?