The 12v trigger is on only when the receiver is on. It's typically very low power, and most often is used to act as the trigger for an external amplifier. Perhaps lower a screen for a front projection setup with a motorized screen.
You could power a 12v fan I'm sure if the draw is low enough. Which is an issue, since most draw is closer to 300mA+.
Yes, that Niles unit would work fine.