Could the GPS be used to aid the autopilot with speed?
The main issue is that we can only get groundspeed from GPS data. Winds aloft aren't known exactly at a particular place, so they could be rather inaccurate -- certainly not enough to leave to the hands of the autopilot. The decision to use GPS data to verify airspeed would lie in the hands of the crew. Anyway, they were too preoccupied to go and check that their ground speed was sort of accurate.

It's not uncommon for winds aloft to reach speeds between 180 and 200 knots. While previous weather reports can be useful, winds can change quite frequently -- the chances of the wind changing is much more than the chances of all the sources of airspeed becoming unreliable.

GPS data is also not 100% accurate, so keep that in mind, especially if only some of the sattelites can be reached.

What the crash came down to was mainly a loss of situational awareness, combined with their lack of experience with actual stall recovery, was the main contributing factor to the accident.