Funnily enough I was exercising a 737 PTU this afternoon over E Anglia at 15,000ft!
In normal operation, the autoslat system automatically drives the slats out from extend to full extend about 5-10kts before the stick shake to give you some extra speed protection above the stall. If/when you accelerate away from the stickshake/stall the autoslat system will return the slats back to extend.
The flaps must be at or between 1 & 10 (strictly between not up and less than 15 because they could be in transit) for the autoslat to operate. This is normally powered by the B system.
If the B system pressure is not available (again look in the FCOM for the precise criteria), the PTU uses A system pressure to pressurise the B sys fluid to power the autoslat system. Note that you still require B sys fluid, so you lose autoslat with a loss of B quantity not pressure.
Moving the Alternate Flaps switch to ARM will not affect autoslat or PTU operation. However, remember once you start to move the T/E flaps down with the alternate system the L/E devices will travel inexorably to Full extend, so the autoslat system effectively becomes redundant.
Just for the info of any 737 pilots/engineers, I have found the PTU not to be totally reliable. In about 200 flight tests I have had 5 not operate. No hard faults were ever found, the engineers simply changed the units. I suspect it was just because they are used so infrequently.
S&L