The short answer is "yes," but be sure the civilian counsel has some experience handling military cases. While courts-martial are similar to federal district court cases, there are also big differences that can throw off a private counsel that is not expecting them.
What about keeping my military lawyer and hiring civilian counsel. Is this possible?
Yes! In civilian courts, once a defendant hires a private lawyer, the public defender must withdraw from the case. In military courts-martial, the accused has the right to have both a civilian lawyer paid out of your pocket AND the designated military lawyer at no personal expense. A lot depends on the personality and style of the civilian lawyer, but even with years of prior military experience I have found as lead counsel that keeping the military lawyer on the case is a big asset. The military lawyer may not be as experienced, but s/he has inside information about the judge, the military prosecutor, the Staff Judge Advocate, how similar cases were handled in the recent past, recent case law, tracking down military witnesses, processing chapter discharges in lieu of court-martial, and other information. It is the best of both worlds - two offices working together to give you the best possible defense team!