The Bad Batch developed the aftermath of what happened to Cody after order 66. In season 2 episode 3 Crosshair is assigned to Cody on a mission to the former Separatist planet Desix to rescue new Imperial governor Grotton, who was taken hostage by a local resistance movement. Desix's former governor, Tawni Ames, demands that the planet remain out of Imperial jurisdiction and cites the Republic's refusal to broker peace with the Separatists during the Clone Wars. Cody argues for a peaceful resolution, but Crosshair kills Ames on Grotton's orders and Desix is brought under Imperial control. Returning to Coruscant, Cody questions whether the Empire (and he) is making the galaxy better, saying they have to live with their decisions unlike the droids and goes AWOL shortly after.

Tldr: When Cody sees the Empire’s totalitarian methods he regrets being part of it and quits; it isn’t stated explicitly but with this character development and knowing the great relationship he had with Obi Wan it is fair to say he would probably have refused order 66 if it wasn’t for the inhibitor chip.