The grunt noise is probably the pump engaging. It is failing some sort of self-test, and might not be a wheel speed sensor at fault. I had a faulty valve block on my Alfa 156 with VDC (Bosch 5.7 ABS with ESP, same as the Stilo).
Or, I suppose the sound could be the brake being applied to a wheel that the system thinks is spinning or sliding, since it has ESP as well.
I think the first thing to do is to check the wheel speed sensor rings for obvious faults (rust, debris), and then connect to
MultiECUScan etc. for a diagnosis.
Has the steering wheel been off recently - is it possible that the steering angle sensor may need to be re-zeroed?
To answer your original question - yes, ASR is just software programming in the ABS unit. It uses the wheel speed sensors, possibly the yaw sensor and steering angle sensor, and can also request a reduction in engine torque from the engine ECU. Theoretically the 5.7 ESP can also apply the brake to the spinning wheel, transferring the torque to the other wheel, but in practice it doesn't seem to achieve that (perhaps yours is trying!), and just reduces engine torque instead.
I once timed a series of takeoffs on a race track with ASR off (in my first Stilo) and with it on. I can honestly say that the variation was within measurement error. Without ASR you get a lot more drama, but with ASR it's just as fast.
VDC/ESP (stability control) cannot be turned off. It will prevent the car from spinning or sliding, by braking individual wheels, and is quite magical. That's just software in the ABS ECU as well.
-Alex