Wikipedia is often not a good source of information, especially to the more arcarne stuff.
Boeing 737 RNP approaches do not need any GPS actually, boeing got an FAA (and EASA) approval to fly any RNP approach including GPS approaches as long as the FMC computed ANP is sufficient, no GPS updating is needed for RNP 0.3, it is however needed for less than 0.3. The FCOM says about the IRS outputs: IRS outputs are independent of external navigation aids. GPS is such an external navigation aid.
Over a longer flight you can actually see how the IRS position (select POSition on the EFIS mode control panel) very very slowly moves away from radio and GPS positions. Oh, and there is of course no automatic initialization, you still have to supply the current position to align the IRS, same as in the old classic 737s.