I'm struggling to find an explicite statement to that affect that the GPS doesn't update the IRS for the 737 but I'm likewise not able to find anything that aludes to the contrary which I would think there would be if that was the case. There is however quite a bit about the GPS, Radio and IRS independently updating the FMC.
My course notes say -
Multi-mode receiver 1 (MMR 1) and MMR 2 have data buses
to the ADIRUs. The MMRs do not supply any data to the
ADIRUs. The data buses are for future use to send
global positioning system (GPS) information.
As far as I know the MMR (GPS) position still goes directly to the FMC on the737NG, A330 however, GPS position goes via the ADIRU's to the FMGEC's.
As to the accuracy of ADS-B, its is still linked to the RNP and as such the MEL for both systems inop reflects this.
