Would it be my dream come true if I turned on my Leica CS20 running captivate, and it connected to the Reach RS+ through bluetooth and so I could use captivate software to carryout my survey??
If the Captivate software can use generic, non-vendor specific NMEA-input, then it is very likely.
Or you can try running the survey with FieldGenius…
Microsurvey is owned by Hexagon, who also own the Leica Geospatial Division, so the compatibility is generally good. Just note that leica sometimes soft-lock their units to on-brand software and want money to allow them to communicate with 3rd party software.