Yea, it sounds like an indication of failure of the engine cooling fan or Fan Module. Any time the A/C is on, the fan should be turning, at least at low speed. If it is not, then either the motor or module is bad.

Start the car up when it's dead cold. Fan should be still.
Turn A/C on and interior fan on low or medium speed.
If the outside air temperature is above about 36F, the engine fan should turn about 120 rpm.