The Univolt will try to recharge the battery using the power from the inverter - albiet inefficiently. This plus whatever parasitic load you might have on the 110 volt side will drain the battery faster than needed.
Movies or music should have a low amperage draw - you might get away with using an existing cigarette plug, or you could install a new cigarette plug off the wiring from the battery to the univolt. Install a fuse!
It is much more efficient to use a 12 volt
TV and DVD player, than to use an inverter.