First any parts for the new 5c won't be available for quite awhile.
As to the battery its' self its' just to soon to tell if Apple altered things so the connections are not compatible. You will need to wait for the IFIXIT teardown to see what is discovered.
If you have a working battery in your phone now I wouldn't waste the money (or risks of damaging) swapping the battery to try to get the few minutes more of life the slightly larger battery offers if that was your intent.