That I cannot tell for sure. Maybe a read into the changes between Android 6 and 7 can reveal some news here. Hardware won´t change, but changes in the BT stack could bring advancements and solve issues.
There are alternative OSes available for FP2 based on Android 7.1 (LineageOS). But switching back and forth for evaluation is time-consuming.
You seem to keep it practical cordless which is fine for a mobile handset. Many users here rather report problems with cabled headsets, there were mainly issues with BT in correspondence with car hifi or wifi.
Edit: correction in accordance to @AnotherElk reply.