Generally no, but if the cut out contacts were stuck closed then current could flow to the generator and cook the armature. You would see smoke coming out of the generator and it would be very hot to touch. Most likely something else is draining the battery or the battery itself is faulty and draining internally. You should have a battery cut off switch fitted to any car that sits around a bit to ensure it is safe. Need to do some testing here to find where the problem lies. Connect an ammeter or voltmeter in series with one battery cable and see if you get a reading with everything turned off. Should be zero really on a car like yours providing there are no add on electronic modern items fitted. Regards, Kevin.