There are various threads on this site detailing some of the challenges for dual-military couples. Check them out for more stories. Yes, it is absolutely possible you would be stationed on opposite sides of the country. The detailers will TRY to keep you colocated, but there are no guarantees. You should also know that while either of you are in training, you may not request colocation... meaning if you get a flight spot, you will head off to Newport for OCS for 13 weeks, then down to Pensacola and who knows where else for 2 years for flight school. It is possible your wife could get stationed at a hospital at a flight training base, but if you move to another training location after 6 months or 6 weeks, she will not move with you. No difference in the policies if you were to enlist.
My husband and I are both P-3 pilots, we've been married almost 6 years, so it can be done. We were stationed together on our first sea tour: six months together, one of us deployed for 6 months, 6 months together, the other one deploys for six months and repeat. But then there are the extra detachments, workups, trips, etc during your non-deployed time as well.
I am not trying to discourage you, but I hate seeing flight students coming in complaining about being separated and/or not getting orders together. You need to know as much as you can before signing on to this lifestyle.