Could a bad power window switch drain the battery?

1993 Altima GLE. I know they had issues with their power window switches. Back windows have both rolled down automatically and they won't go back up. Each time this happens, the battery dies. Am I dealing with only a bad switch, or do I need to worry about a short as well. I'm going to recharge the battery and start checking for electrical gremlins, but I'm hoping that the switch is the only problem.