They might have enough, there are 122 P-8s in service, and surely the Navy has > 1 pilot per P-8.

I can’t speak to any material differences between the P-8 and the civilian 737, but legally this still seems problematic. The DoD isn’t required to type certify their aircraft, and it doesn’t look like the P-8 or the C-40 (also a 737) are type certified as a 737, which means their pilots probably can’t legally fly a 737 civilian model. I could be wrong though, the FAA’s website is hard to navigate.