Kind of. If you're an ardent F2P player that never ever ever pulls on Sugofests, then he's necessary as he's the best F2P Driven booster in the game. Thing is though, Driven is basically not a coherent class unless you've got the devils luck on the few pulls you do, or are already P2P to some extent to begin with. If you do pulls, then Caesar Clown is easily superior to Shiki as a Driven booster(2 turns vs. 1 turn of 1.75x to Driven units), making him replaceable. Shiki's orb manipulation aspect can be overlooked because Driven has a very large number of orb manipulators/matchers, like the Kid + Pica combo mentioned on this page.
I still figure he's worth having as one-of either way, though.
While I wouldn't say Shiki is necessary to have, he does serve different functions from Caeser and he's absolutely worth farming for Driven teams.
Shiki has a lower cooldown, which allows him to combo with maxed Legend Doffy for quicker runs when you only need one turn of burst. And having both orb manipulation and class boost in one character frees up utility slots on your team.
He also acts as a good STR slasher orb manipulator and self booster, which is kind of rare.
Thanks for the thoughts. Seems like he'll be used if I have him and skill him up, but if i don't, chances are I could make it work in some other way.