I'm no expert, either. Maybe someone more knowledgeable will chime in.
I hope that future versions of the browsers would have an option to disable battery level reporting in HTML5. That would seem to be the easiest place to stop it.
03 Feb 2015, Know the Battery Status of your Visitors Mobile Phone
I still question the premise that battery performance info can identify individuals out of millions of users.
Sounds very ambiguous.
More would be easily gained by IP address in most cases.
Privacy mode has no impact on how visible you are on the internet.
Privacy mode only prevents the data from your browsing session from being stored on your local machine.