If you are applying 12 V directly to the fan and it does not run, then the fan is bad. Make sure you bypass the switch when you do the testing. The fan keeps the radiator, and hence the engine, cool whenever it gets too hot. The aux fan usually comes to the rescue when the car is idling, and always comes on with the A/C. YOu will not be able to run your A/C while idling if it is hot outside if your Aux. fan is not working. (1) The air will come out warm, and (2) Your engine will overheat.
YOu can do without it, if you remember to turn off the A/C when you are riding at really slow speeds or idling. It is a real pain and very dangerous since you may forget.
I bought a cheapo Taiwanese aux fan off eBay and installed it with my little sister's help. I have had no trouble whatsoever.
If you liev in Miami, like your handle suggests, I would say you need to change that fan urgently.