He only fainted after the battle with Killer iirc, and that wasn't even because of the battle itself.
If you want to say he had a hard time against King, fair enough, but he didn't faint: he is willingly resting, even took the time to take his bandana off before doing so.
Take a look at the Sanji panels in chapter 1035 to see what fainting looks like.:yasu:
Zoro might faint for a second time this arc after Killing Kaido, depending on how the mink drug wears off.