Just for the record, a Jamma+ game is not a game with a hard drive... it's a JAMMA game that uses more buttons than the standard JAMMA specs allow.... so any 6 button fighter for instance is JAMMA+. The extra buttons are put on a "kick harness" that attaches directly to the board.
So JAMMA+ and a hard drive game (or a game that uses a CHD image) are not one in the same... just don't want you to be confused.
To answer your original question, yes, you can run hard drive games with a Multi-JAMMA board. As CheffoJeffo quoted, you just need to wire up the "extra" buttons to kick harnesses.