[Tannaton]

It's a No... the non Volvo system interprets the basic Canbus signals to operate the lights.

The Volvo system has intelligence within and can be programmed, as well as interact with other systems on the car such for bulb failure, traction control, parking sensors etc.

The big clue is the fog light delete function involves cutting the wire to it and inserting the relay, the Volvo trailer module does this through the software.

As said above there are a number of features on the Volvo system :

Rear fog light off (some third party systems have this)
Parking sensors off
Trailer Stability Assist (not available any other way)

The Volvo system is not expensive to buy and have fitted to a third party towbar.