Don't know about the AF, but for the Navy, the only guy who can violate you is the CNO, so the FAA would have to petition the Navy for the violation. HOWEVER, if you do hold FAA certificates, I believe they can still go after you. Not necessarily for a violation, but as far as pulling said paperwork if the act warranted it.
Seeing as I was MC for a flight which received over 200 violations off Long Beach while doing a ISAR test around 1987-1988, I feel a little qualified to address this point....
The FAA is supposed to forward any violations for the military to the appropriate service. The service then is supposed to investigate the matter. If the service decides the violation was due to operational necessity, the service takes the violation. A component in the chain of command can accept the violation. If the service decides the violation was due to negligence or not required as part of the mission, it can assign the violation to the aircraft commander and/or mission commander. The service then decides what action to take against the individuals and their military flying status. If the service assigns the violation to the crew, it may or may not release the name(s) of those involved to the FAA. If the service releases the names of the crew, then the FAA can take action against any FAA certificates they hold.
In my case the violations were reported to the appropriate CNO staff office and forwarded down the chain to AIRPAC and then CPWP. CPWP took on the violations and it ended there. However I will say my case was pretty unique in that we knew we were going to get the violations before we even took off.
We were conducting a test of ISAR (it was new then...) against ships and shore based targets off Long Beach. We had ships at anchor, ships underway, ships next to the pier and objects on the pier and slightly inland. It was a test that supposedly cost close to $20 million to set up and conduct. It had been in the works for over a year and required extensive coordination. We had air space reservations with the FAA which they canceled about an hour before we were scheduled to take off. Due to the winds, they said they needed the airspace for the airline approaches into LAX. Rescheduling the test would cost huge bucks and take months so our Admiral (Commander Patrol Wings Pacific -CPWP) told AIRPAC he was going to launch it anyway. AIRPAC concurred and off we went. We said Due Regard and MARSA to ATC and ignored their vectors out of the airspace. We were flying a 20 mile racetrack with the south end violating the Class B (TCA back then) and their approach corridors. Every lap - "Navy RCXX turn right heading XXX...Approach, Navy RCXX can not comply, we are due regard and MARSA at this time....Navy RCXXX you're violated......Approach, Navy RCXXX roger..." There was also a whole lot of off colored remarks thrown our way by the airlines as they were vectored, held and delayed but our little operation......
I don't know if it is still a point discussed during annual instrument ground school but they used to emphasize that if ATC ever asks your name you don't give it. You only give your aircraft call sign and said to forward any questions to AIRPAC or AIRLANT (it might have been the type commander?). If ATC gives you a phone number and asks that you call, you are supposed to not call and report it up your chain of command for action. It was also part of the training for SDOs, etc not to give out aircrew names. Base Ops is not supposed to give out the names either and military flight plans filed with the FAA are not supposed to include PIC names. At least this was the way it was taught during my last Navy instrument ground school in 1996. I don't know if it has changed.
Military and government pilots (to include the local PD helos) are supposed to observe FARs to the maximum extent possible but under federal law they can deviate when required. That is why flight violations are supposed to go to the service for investigation and assignment.
Edit: I just saw that while I was typing my book, Nittany said the same thing about not giving names.