What is the correlation between RNP level and the CDI indication?
The Performance Based Navigation concept allows to optimize the instrument procedure design with the aircraft navigation performance.
This concept is used en route, to reduce aircraft separation, and in terminal area to optimize arrival and departure procedures. The utmost development of Performance Based Navigation for approach, missed approach and departure is known under different names.
FAA initially referred to RNP SAAAR Operations, SAAAR standing for Special Aircraft and Aircrew Authorization Required.
ICAO now refers to RNP Operations with Authorization Required (RNP AR).

The estimation of the aircraft position is performed by the Flight Management System based on different sensors: Inertial (ADIRU), GPS, radio navigation (DME and VOR).
The FMS computes the best aircraft position estimate based on the following hierarchy of navigation modes:


GPS/inertial,
DME/DME/inertial,
VOR/DME/inertial, 
Inertial only.


The RNP capability depends on the availability of GPS/IRS integrity.

The GPS integrity mainly depends on the number of received satellites, the FMS will calculate the GPS estimated error as a function of the number of received satellites and which satellites among the most appropriate for the aircraft position.

The ADIRUs are capable to evaluate their own estimated error that they send to the FMS, similarly the FMS itself is able to calculate the ADIRUs  drift error based on previous ILS landing(if any)  as he compares the ADIRU position to the real aircraft position while on the ILS, This error is reduced to a mean average drift per hour of flight.

The FMS therefore is able to calculate an Estimated Position Error (EPE), thus allowing the CDU to display both the Required Precision, and the Estimated precision

With respect to the HSI, it displays a route as well the approach calculated by the FMS, within the estimated precision which normally is better than the required precision, the pilot is supposed to be on the route and not one dot  or 2 dots apart. When the CDI is centered you are within the Estimated Error;  However indeed if the CDI is not centered the error is augmented as you say in the question, but you should not add the RNP but the Estimated NP that shows on the CDU, because the FMS calculations are normally correct.

Of course if your equipments are faulty and mysteriously the multiple faults are not detected you may be neither within the RNP nor within the ENP.

Please refer to the following website for more details:

https://www.theairlinepilots.com/forumarchive/aviation-regulations/rnp-ar.pdf