Denti:
FPO, the 737 does not have internal IRU updating and is 0.10/GLS certified as standard equipment. The GPS receivers are part of the MMR, not part of the ADIRU. And one can see quite a bit of IRS run-off after a lengthy flight, just recently after a 6 hour sector had the IRS's around 2 to 3 NM off the FMC/GPS/radio position, and the ANP was still 0.02. There is no need for internal updating as the IRS is only used for its short term stability and the GPS provides long-term stability. Filtering based on that principle is done in the FMC.
Any 737s that can qualify for RNP AR IAPs of less than RNP 0.30 have to have FMS position updating to the MAP, so that in the event of a loss of GPS (sats, not airplane receivers) the FMS position derived from the IRUs has zero drift at the MAP.
None of this is required for long-range navigation.
When I flew the early generation 767, which had no updating, and no GPS, our IRU position error was typical around 1 mile for all three IRUs at the end of a 6 hour flight.