Yup.

Couple of additional things to take note of. You do not have to run the fans at 12 volts, if you run them at lesser voltage they will spin slower, an thus be quieter (if that's important to you). Though there is usually a minimum voltage that they will not operate under.

You will also see talk about 3-pin and 4-pin fans. Don't worry about it. For your use case, ie running it of a separate power supply, it makes no difference. The 4th pin is use for PWM (pulse width modulation) which is a different way to modulate the fan speed. If you're not using it 3 and 4 pin fans operate exactly the same way.