Well, in that case I think you are asking the wrong question then, dear Rennaps.
I can only think now of two possible interpretations to your enigmatic query my friend:
If, by CAN, you meant if the airplanes know "how to" fly an RNAV / RNP, well, the answer is YES for as long as the NAV system is designed to make the respective updates based on GNSS, DME/DME etcetera or;
If by CAN you meant: is it authorized by ATC, well, in that case you CAN'T read, otherwise I don' know which part of (quoting myself): "The Basic‐ RNP 1 navigation specification is intended for similar operations outside radar coverage".
One of the requirements almost in every major airport in the world (class B or Class C airspace) is to have an operating or fully functional Transponder. I know you are very experienced so I assume there is no need to explain the inter-relation between xponders and ATC radars right?. As a corollary, I think you should change the term ( quote) "Just RNAV 1" since it is a lot more restrictive than RNP 1.
Last but not least, I would say YES to the question if an airplane CAN fly an RF fix to radius approach but, you would have to select it from your airplane data base and select a lateral mode such as LNAV or similar. I can assure you the airplane will master RF better than any pilot could do. just for the record, the plane can go to an as low as ANP of 0.01 ~ +/- 18 meters.
Warm regards my friend