Will a broken timing belt cause engine damage on a 1999 Mitsubishi Galant V6?

Without a doubt! Most people make the mistake of trying to re-crank a car after the belt has snapped because the car just "dies" without warning. The re-cranking of the car is what causes valve damage in the engine because the belt, which controls the timing of the engine, is gone. Engine parts are now just flailing away hitting against each other causing internal damage.