FMC fuel entry - MD11 with MEL 28-41-xx
If the FQIS is giving an erroneous indication, it is a simple matter, after starting one engine, to go to the FMC INIT page - FUEL, and deselect FQ (fuel quantity).
By doing this, the FOB is calculated only from the original (blocked) FOB - FF (fuel flow) (as determined from the FF sensors at each FCU (fuel control unit).
By using this method, there should be no incorrectly computed GW, thereby giving erroneous performance/speed data to/from the FMC.
However, your questions asks specifically of the B737/A320 FMCs; I would like to think those FMCs have a similar capability.