OP, short answer is no.
I'm active Navy now. I can tell you that with our current DoD budget, on "continuing resolution" we've had to cut a great deal of training and recruiting across all three branches (Department of the Navy, United States Marine Corps, look at your emblem jarheads).
Currently, the Navy is looking for anything (up to five years back) that you did that they can end your service for. Most waivers are being denied, that is for medical, legal, financial and AFQT. The only exceptions are in the intelegence and nuclear power fields. To my knowledge, this is also across all branches. There are enough people trying to get in now that it will come down to you OR them, and if only one of you has astma... Sorry kid.
I do wish you the best. If this is your dream, you can ask. The absolute worst thing a recruiter will say to you is no.
~V
EDIT: Just saw this, way off topic but... EvilWizard and davidmcbeth3... LOL! Evil, I'm glad you're honest. dm, All I have to say is that if you're having those kinds of problems there was a breakdown in training at multiple levels wherever you were stationed, not just in flightline safety either. What universe do you live in where B-52's fly and deliver nukes? Or where a refuel team also loads ords, directs aircraft, and ok's takeoff? Even the Navy has four groups of people to perform those tasks, and we merge several jobs due to manning restrictions.