It would make it harder for the average USC applicant to join in. The military has complained in the past that although they haven't had trouble meeting their recruiting quotas, the quality (intelligence) of recruits is not that impressive. They want more smart people. Let's be honest, a great portion of applicants are individuals who didn't know what to do with their lives or weren't smart enough to earn academic scholarships so they saw the military as a great option to pay for their studies. Therefore, taking that fact into account, since most dreamers are intelligent individuals, they would not have much trouble getting in front of the line of desired candidates in the eyes of military officials unless, of course, they have some medical condition.

P.S. : screw the ARMS act.