Yes, it definitively goes faster. It's just that these boards are calibrated once for what voltage gives what belt speed with the motor during that production cycle at the factory. I would not be surprised if they do it with the belt unloaded and only for one of the motors in the entire cycle (since they use the same motor type for all of them).
But it’s not far fetched to think that motors vary and that they should either calibrate each treadmill separately under an average load, or have this type of sensor to adjust the speed constantly like the more expensive ones.
Big caveat: The above is just my assumptions.