The short answer is, no, your fiancee will not get in any trouble with the military for marrying you...as long as the marriage itself is legitimate.
What I mean by that is that of you're marrying because you want to be married for love, to build a family, etc., your status will not cause him to have committed a crime (though you should straighten that out as soon as possible).
If, however, you are marrying for no other reason than to stay in the U.S., and the military discovers this, he'll be in trouble for having a "contract marriage," i.e., a marriage arrangement designed to subvert U.S. immigration law, where no legitimate marriage exists. This is evidenced by people not living together, holding themselves out as single, instead of married, etc.
If that happens, he'll likely be sent to court-martial (military criminal trial).
But, of a legitimate marriage, there are no worries.