I was lucky enough to complete 2 yrs service (RM) before going to uni. In my 3rd yr I authorised my own loading onto flying grading. Never wore a uniform (apart from weddings and funerals) for 3 yrs - and got paid even more for being in London.
There were a number of other service personel - mainly 'midi-matelots' - and, I know one of these guys is currently flying harriers fm Yeovilton.
It's a great idea - but, I would take the uni degree first - cos you'll have a great time and for all the other reasons the other responses have identified. Good luck.
(Maybe the FAA are more enlightened
)