I have done this before, if I want a pot of tea instead of making individual cups. For my fiance, who drinks orange pekoe, I stuck a few bags in the pot, nothing in filter basket, and let the water drip into the pot and keep it warm all day. After about the first cup, though, it was too dark for him, so you might want to take the bags out after the desired color is reached. I make my tea (green tea) in the pot sometimes with the same method, but I prefer to leave the bags in all day long.
Have you considered an electric tea kettle? They are used very commonly here. I often forget about mine, but it will never boil over.
If you get one with a mug, you could stick the bag and sugar if you use it in the mug the night before, then the coffee maker would drip down in the morning, steeping the tea. If you are unable to get one with a timer, there are timers that you can get for electrical outlets that automatically start or stop power to anything plugged into them.
Something like this might work (but does not have a timer):
Two to Go Coffeemaker is $29.95 was $80.00