Wrong Terms
It's not Predictive Windshear detection, but Forward Looking Weather Radar windshear detection. The Wx radar can only detect presence of actual windshears ahead, not predict them. We all know the track record of weather predictions...
Yes, it takes some radar reflectors for the Forward Looking Windshear weather radar to do its job, in the form of precipitation, or even blowing dust. It uses the doppler principle to detect wind shears, of course.
IIRC, the reactive Windshear Warning System installed on the MD-11 by McDouglas is a separate computer, and not part of the GPWS, FWIW. That's also what they delivered on the MD-80 at the time. The FLW Wx radar came along a year later. Carriers could have retrofitted FLW into their Wx radars in addition to, or in place of, the reactive system.
GB