Ok, may be repeating people here but this is my 2 cents.
To me the battery is just a special effect, no matter who really has it. Yes it is an object that can be taken away (remember that, so if you did write it up it'd be independent (IIRC). Also it should have invisible or "kept in pocket dimension" depending on who your writing it up for.
I agree with the fact that the ring should be "REC only when touching battery" and just use the battery as an object without a write up. Not everything has to be written up for a game, can get old and tedious. Sure the Reff should go over it with the Player to see what can and can't be done with it and it kept in that context.
OH, and also remember if your thinking of Kyle's ring it can do 3 things now...it keeps a small charge outside of the normal charge, can only be used by him or a family member, and IIRC it can create duplicate rings (or did he give that one to Jade/Stewart..don't keep up with GL that much)