Yes. It's the exact same a/c as the current production MV-22B with the addition of increased fuel capacity, HF radio, some pax related equipment in the back, and different paint.
The Googles say the Osprey-variant has ~15% less range than the C-2. I assume some smart people decided that the difference is negligible for most places the CVN operates, especially with refueling capability.
Also, will be interested to see mission-creep set-in, as the CMV-22B will be capable of operating from many, many more ships than just the Carrier. Off the top of my head, I'd think the LHD/A, LPD, LSD, LCS?, and DDG-1000 are likely NATOPS certified to land an MV-22.