During Navy basic training there are three separate uniform inspections. Everyone is lined up in front of their racks. The inspector, usually a Chief, will tell you what uniform to put on. You then have two minutes to get that uniform on correct to every miniscule detail.
The Chief then goes...
1. If Big Navy decides it "must be done," they will do it because they own you. Basically, you're an investment and they're going to take care of that investment.
2. Think logically. Do you think they have enough staff to pull wisdom teeth of every recruit (about 400/week) that comes through...
Techinically yes. However your recruiter needs to put a chit through their chain of command which take time. Call them NOW.
Next time you make a committment, think it through. Consider reserves.