It does. It drops the air inlet temperature by a significant margin, which fools the motronic into thinking it's taking in colder air. I think the motronic enriches the fuel charge slightly to compensate in the open loop range.
I can't remember the exact figures, but when I measured the air temp value with the GS911. Without the accelerator module the air temp was reading normal ambient temp say 21degC When the module was fitted the temp dropped to a value significantly below freezing.
Colder air is more denser than warm air, so to maintain the same fuel to air ratio the motronic would need to pump more fuel. This only works in the open loop, as the Lambda probe will cut back the fuel in the closed loop to maintain the correct emissions value. Irrespective of the air inlet temp.
Anyway I think that's how it works, I'm sure someone will be along in a minute to correct me if I'm wrong.
I think in your case the module may have been over fuelling, in the mid range, which could be why without it you have seen Improovements.
Ian