Obviously no official FDR but the AAIB have on occassion recovered information on the track of an aircraft prior to incident from onboard GPS equipment, both inbuilt avionics and the likes of Sky Demon running on an iPad. This work is often quite involved in the case of water damage when flash memory chips are carefully transplanted from the water damaged equipment to a working version. However it can be done.
Also at risk of stating obvious, instruments e.g. ASI, VSI may also fail in a way that indicates airspeed, vert. speed at time of impact.
Chaps at AAIB are highly skilled and very thorough. Whether or not they have the resources to justify such an investigation into an SEP with 2 POB crashing into the sea in IMC is anyone's guess.