VX-351 is passive; obviously it receives power and all sorts of voltages via the DB25 connector but it doesn't NEED any external power and there is no power supply or way to add. (I can't speak for the VX-352 but it's likely the same).
I think the cable that comes with the rack mount kit is to 'jump' power from the VX-351 (which gets power from the Voyager) to the CP-251, thus making it unnecessary for the external power adapter. But I don't have a "CP" so not sure.
I think Erik has experience with this so should chime in shortly.
Moog Voyager Select, Taurus 3, Opus 3; Oberheim Son of 2-voice; Sequential ProOne; Waldorf Blofeld; 48 of MU Modular; Kurzweil 250; Hammond M3; Fender '75 Jazz, Tony Franklin Fretless, Hoppus, Roadworn Jazz; Yamaha Att III; Mesa Amps; MF101,102,104M,105M