Maybe yes, maybe not!
I actually give it 50/50
In fact, I feel there are majorly two reasons as why we give Mihawk CoC
1- Because Hancock and Doffy have it. And thus, by default the Strongest Shichibukai should have it when two shichibukai weaker than him have it
2- The domino effect. Rayleigh has it, so Zoro probably will unlock it, and then Zoro's main goal (should have it)
But then again, nothing is guaranteed. I wouldn't be surprised if Oda made him lack CoC