It is a real guitar. Drew Sarich does play guitar--he has his own band called International Victim: www.myspace.com/victiminternational
The guitar is over 100 years old. Originally he was to bring it out earlier in the scene (the one where he reads the newspaper) but the director decided it would be too distracting. So then it was to come out on one of the carts during the building of the barricade, but seeing how old and valuable the guitar is they decided that was not the safest course of action. Ultimately it was decided that Drew would walk off and get it (which seems a little distracting, but I'm over it). But yes, he does play it up until Marius' interjection into the song and Grantaire stands up and hands it to another student who removes the prop to safety.
Plince! Plince! Nein! T-Rex!!