You would need to notify your recruiter of any changes in status, including dependents. This quite possibly could delay your ship date. Depending on if she has dependents it could also make you ineligible for enlistment. For example, she already has 3 kids, then you pick up 4 dependents, Navy doesn't like that. Any more than 2 requires a waiver, ISTR.
Seriously, boot isn't that long. Just wait. Heck, even waiting until after A-school isn't going to kill you. It's less than a year. Also, between you me and the 200K other guys that read this board... wait. If she isn't fond of you being away for just 2 months at Boot... well she REALLY won't like it when you are deployed for 6+ months in far away seas with no contact. Navy life is full of separations. Best she learn that now, and sees if she can hack it. Many women can't. Better to know that now when it's less financially and emotionally damaging. Just some advice from someone whose been there, done that and wishes he didn't have the tee shirt.