Too much equipment, too little time! Airbus variants that use the Honeywell ADIRU, the GPS updates the IRU directly, which is why that unit has such high accuracy values. How the Smiths box handles this, I am not aware.
With regards to a non-GPS RNP procedure, yes, that would be considered an ANP approach, and as long as the ANP value does not exceed the RNP value, than this is all good. The 777 has the express feature that on disco of the GPS, the box defers to ANP.