No. According the the T&Cs any stay (consecutive nights regardless of check-outs/check-ins) using points (including Points & Money) does not earn credit/points. This will count for multiple rooms too. Of course this all depends upon the property processing everything correctly which is not guaranteed but may be corrected later.

You best bet is to gift the point stay to the other person (make them the registered guest) to separate the stay from your reservation. Asking nicely when checking in, they may grant benefits to the second room, but absolutely not required to do so. If you're looking to get points for any incidentals, give the other person charging rights and have them bill everything to your room. Or you may be able to get the front desk to transfer all charges to your folio at check-out.