I suppose there are a number of variables to consider (what your emphasis/specialty is, your areas of competence), but yes, most likely you are looking at teaching at some religious affiliated school in a religion department - maybe teaching a philosophy of religion class or something like that. I applied at UBC (British Columbia) and they explicitly mentioned that they DO NOT recognize A.M./divinity degrees. I don't know if a degree from Yale, Harvard, U of C etc... would serve as an exception, my suspicion is that it would. Also, if you want to a program like U of C you are looking at getting an actual Ph.D which would certainly help when applying to more secular schools. Still, I'd have to say the prospects aren't great (you're getting pigeonholed into a certain niche) and the prospects already aren't great to begin. I hate to discourage you from your dream but these are some things I would CAREFULLY consider before adding to your debt.
One of my professors graduated from U of C, got his A.M. and Ph.D there. He is the school chaplain, teaches theology/Christian History courses/Environmental Ethics. He also got his B.A. in philosophy after a while, I don't know if thats something my school encouraged him to do or not.