The circuit is simple. The LED is connected to the 24V source (AKA 24+) as is one of the 2 output terminals for the fan. AKA 24V is constant hot or live. There is NOTHING between the main input and that output positive side to blow, fail or otherwise. It's about as direct as it gets. The GROUND is what is switched on and off by the FET. Only when the FET turns on, can current return through the circuit from Positive to Negative (ground).
The LED is wired in parallel to the terminals for output. So the LED is a true indicator of when the FET really is on or off and will work even if NOTHING is connected to the fan port.
As such, if you really want to make sure- disconnect the thermocouples. That should force the board into safety mode and not being able to read the thermocouples forces the extruder fan on instantly.
So again, just disconnect the TC if you think there is something wonky- that will validate the FET is blown and that's QUITE likely on a rev G board since the FET is rated around 200mA on a good day.
Any short or excessive load will blow them sky high. It's a suspect design with no margin for error. Sure it works most of the time but enough failures happen and it's dumb to kill a board over a stupid fan.
This is why I actually like older Rev E clone boards. They have 76A rated MOSFETs even for the fans. If you kill one of those MOSFETs consider me impressed.