Myself and another FT member actually did this a couple of weeks ago, albeit travelling in F.

I had a RFS ticket LHR to INV, and a cash booking INV to LHR to EWR (and onwards to SJC via LAX after an overnight).

I checked in at the First desks, gave them both PNR's and told them I didn't want to take my bag to Inverness. I asked to check my bag straight onto the 2nd flight on the 2nd PNR.. The agent did this with no issues.

My travelling companion who checked in separately did the same thing (with the same flights) and had the same result.