the electric fan does more than cool the tranny. When idliing or stuck in traffic it comes on when the engine temp rises. It's also there to help dissipate the heat from the A/C. Yes, it needs fixed.
Turn on the AC and see if it comes on, if so then it's probably something in the temperature switch. You could also run 12V directly to it to see if the fan is really dead, or if it's the relay.