There are no seperate licenses in the US so it will be added.
Anything involving a 61.75 requires a ‘letter of verification’.
As in you can not add a rotary to a fixed wing certificate if the underlying fixed wing EASA has expired.
So you’ll need to provide evidence that both the EASA fixed wing and the EASA rotary are valid and not under suspension at the time of application.
Your US Certificate will read Private Pilot on the front and on the rear:
Single Engine Land
Rotorcraft
In any case DO NOT contact a FSDO. They are regional offices and depending on location may not be very well versed in License validations. Also you may speak with a FAA inspector who has randomly been appointed phone duty that day.
That’s no garantee for success.
With these types of questions always call the Airman Certification Branch in Oklahoma which is the head office.
Get their opinions in writing (email) and then select a FSDO to visit for your license validation.