Sure, but then it would be in the microbes in the dog’s bloodstream, right? Not freely floating available to work for oxygen exchange (which as you rightly point out, it doesn’t really do anyway.)
The day I learned how the blood “knows” when to let go of oxygen in the bloodstream, I heard the angels singing and sat there in awe of…just everything. So freaking cool.
I thought I was making a little headway, gently pointing out that carbon monoxide is even “closer” to carbon dioxide, and hydrogen peroxide is “closer” to water, than chlorophyll is “close” to hemoglobin, and we all know that those “close” molecules don’t act the same way in the body. That did elicit a few chuckles and nods. Then they brought up the dog. :smack:
Smacking them in the face? Yeah, that might work. Or it might just make me feel better. 
(At least I’m not missing anything obvious. Thanks for confirming that. I suppose there’s no real debate here and I should have just put it into the Pit.)