Yes…

Yes it does.

To clarify, the battery new battery charger provided with the Canon EOS 1D-X mark II is the LC-E19.  The native battery for the same camera is now the LP-E19.  The camera can also be used with the previous batteries from the original 1D-X called the LP-E4N.  The new charger is backward compatible with the older battery packs, and will charge them.