Doppler from multiple geostationary sats would give you derived heading, speed and possibly location. It's how the Americans tracked Sputnik.
Just a moment please. Sputnik was a polar-orbiting satellite, not a geostationary one. And the Americans certainly did not have any geostationary satellites in 1957.
You can track polar orbiters from the ground using doppler shift, yes. But the geometrics of a geostationary satellite at 36 000 km listening to a comparatively slow target at 10 km altitude do not allow a significant doppler shift.
The doppler shift method (also used by COSPAS/SARSAT) is based on being able to track a continuous signal while the satellite passes the target. On the first pass you can get the latitude (point of doppler shift changing from approaching to retreating) and after the next satellite pass and a second fix you may calculate the longitude.
None of this is applicable to MH370 and geostationary satellites.