Non-pilot military service will not give you a hiring advantage if you are not otherwise competetive with flight experience.
If you are in the competetive range, the military background will probably show them that you already have many of the characterists they want in an airline pilot so it should give you a small edge.
There are a few guys at the regionals you got rejected by the military for whatever reason, and these guys might hold a grudge against military pilots (yes, I have seen this). But for an enlisted guy, this will probably not be an issue, just don't beat the military drum if you get bad vibes from the interviewer.
In aviation hiring the most important factor is flight time; next is who you know.