No. Not unless you want to add Economics major, Physicians degree, Law degree, Foreign Relations major, Business degree, and high school principal to the requirements to be President.
The Presidency is the "top job", and you influence so many things: health care, education, defense, foreign relations, etc. Adding any soft or prerequisite to the job would prevent a LOT of people from being President. The general image of America is that you can be ANYTHING you want to be... if we knock leader of the free world off that virtual never-ending list, then that sends a very bad message to children all across this country.
Besides, If I'm going to be President someday, I don't want the only thing to stop me to be the fact that I've never been in the military.
