I have a battery that says it has a working current of 4.6A and rated voltage of DC 12V I need the battery to power a motor for a fan that says it has a voltage of DC 3.7V Will it work? What will happen?
It will work until something overheats or otherwise fails. The speed of a DC motor is proportional to voltage. If a 3.7-volt DC motor is connected to 12 volts, it will try to run at 12/3.7 = 3.2 times the normal speed. The mechanical power required to drive a fan is approximately proportional to speed cubed. That means the fan will try to load the motor to about 10 times the rated operating power.
If the motor is a brushless motor, it has electronic circuitry that might limit the fan speed or current. However that circuitry is probably not designed for 12 volts input. There is no reason to expect it not to fail.