I don't know, it feels like a bit of a stretch to go from Captain John Christopher to Captain Christopher Pike. Feels rather contrived and more of a play on words as one is a first name and one is a last name. And the ranks end up feeling even more like a pun in the end because an Air Force captain would be the equivalent of a lieutenant in Star Fleet where a Star Fleet Captain is the equivalent of an Air Force Colonel. Yes, it could be possible but as far as good writing, I'm not sure it would go over very well.
"Don't confuse facts with reality."
-Robert D. Ballard