It seems to me that with no federal statute prohibiting a civilian from bringing a firearm on base, there would be no penalty for the civilian if he were to do so, unless, of course, a federal trespassing statute is violated.
The governing publication for the Army is AR 190-11. See page 22, Para 4-5.
There have been cases of folks carrying concealed on Army bases. Military folks are sometimes court-martialed and civilians almost always see the federal magistrate. It's a felony thing.