It was a while ago, but…
If I recall the IRSs do not update, they are a source of input to the FMC. TOGA updates the FMC position to the selected Runway or intersection. DME/DME or Nav updating only updates the FMC. In the absence of that, you will have IRS drift, which would be outside RNP tolerances.
The CDU displays a Radio position, IRS or FMC (best guess) position. Dual FMC option is certified as sole source of navigation.