engfireleft, an overlay approach is simply a normal RNAV approach, which uses a specified RNP.
Completely different from that however is the authorization to fly any non precision approach, without the need for any existing RNAV approach being published, by FMC guidance alone. The 737 FCOM even tells us about raw data monitoring during non ILS/GLS approaches "For airplanes with two operational FMC, two IRS and two GPS receivers (or two DME receivers if GPS updating is not available), or if the FMC is RNP/ANP capable, raw data monitoring is not required." Which means only one RNP/ANP capable FMC is enough to fly non precision approaches without using any raw data source related to the procedure. However we do have to keep within certain RNP limits, since we are no longer able to check with raw data if we are within the limits of the procedure.
Of course you need to train the crews for that, same as you train them to fly ILS, GLS or RNAV approaches.
The approach in itself does not have a RNP value, however if you are authorized to fly it without using raw data as primary means of navigation you most probably have to conform to a certain RNP. The values and certification process are of course something to check with both the local regulator and the OEM.