Even if Zoro wouldn't have been in that state he would have still scarred Kaido.
First, the manga implied his flying dragon blaze has the power to scar Kaido. That's why Big Mom and Kaido were so worried about the attack. There's no need for them to be that worry about an attack Kaido can easily heal from. If that attack can scar Kaido than Zoro's other high end attacks has the potential to do the same. IE: Death lion song, 1080 pound canon, and billion world technique.
Second, there is no evidence supporting Zoro needs to use CoC to scar Kaido. Even Kiku can at least hurt Kaido. Since there is evidence supporting Zoro's none asura attack can scar Kaido than his Asura attacks, which are stronger can definitely scar Kaido. Zoro now has 3 asura attacks.
Would Zoro in better condition beat or kill Kaido? Of course not, but he would give Kaido harder and longer fight, and scar him more. Zoro, while weaken and heavily injured in asura mode, blitzed Kaido and deflected all of his attacks. Zoro in better condition would have done the same if not better in that area. Since Zoro has never passed out from using asura mode he should be able to use it longer and/or several times in battle.
You can see a fresh Zoro would have performed better against Kaido in a 1v1 because he would be able to fight Kaido longer and use more attacks that have to power to scar and weaken Kaido. Since Kaido is stronger than Zoro he would be able to push Zoro to his limit which would still cause Zoro to unlock adv CoC haki and use against Kaido. In the end Zoro would still end up with CoC. But now Kaido would be in worse shape.