Something weird happened in the KOTR fight. I can't exactly remember what happened, but I think this was the sequence:
*stuff happened* --> Cid died --> Shinryu cast the zombie thing that said it is permeating the air --> Cid was revived with Renew --> I could control Cid normally --> Cloud died --> I couldn't target Cloud to revive him, including with Renew --> eventually Aeris died --> I couldn't target anyone now, but Cid was still alive --> Cid spent the next 10+ minutes slowly chipping down Omega until he died.
Disclaimer: I don't know exactly when Cid died. But, I definitely couldn't target Cloud or Aeris once they died, and I definitely cast Renew on Cid to revive him at some point.
During Cid's Zombincibility, Omega never did anything, I assume because Cid couldn't be targeted (because I couldn't target Cid with anything either). I only occasionally saw the " Target Locked!" pop-up, but with no animation from Omega.
I didn't remember the info about Zombie from the Beginner Hall, and I didn't find info about Statuses in the Documentation (can I suggest putting it in the Balancing document?), so the only info I found was from these posts, and it sounds like you should still be able to target and cast spells (like Barrier/MBarrier) on Zombie-d characters.
If you want, you can wait until tomorrow, and I'll try the fight again and recreate what had happened.