No. You have it wrong, and Tim did fall for it - we ALL fall for it, it's a result of the physiology of the human body. He's always ALWAYS doing BAH. Even when the image is him doing FAH. Yet when he's doing FAH visually, we hear FAH. You can prove this by looking away whilst he's doing it - you'll suddenly hear BAH again.
Logic would dictate you change them then
The amount of times you will be mixing and looking at someone's mouth in your life will be minimal.
Interesting phenomena but I don't think it has any relevance to mixing.
That's pretty cool, but I don't think I would choose to spend 25 years of my life researching that
When I'm trying to listen closely to something in order to make judgments on the overall color and spectral balance in particular, I always look away from the screen and even close my eyes a lot of the time, because the unnecessary visual stimuli of the waveform, or the cursor, or whatever else, has a very definite negative impact on my ability to make good decisions. That said, despite the fact that visual stimuli does play a role in mixing audio, I think your statement is still 100% correct, as the McGurk effect seems to only describe the interaction between hearing and vision specifically in speech perception, not any or all audio in general.
It is very easy to temporarily trick yourself into hearing things. Hearing a subtle eq change when turning knobs and later realizing it's bypassed. Fiddling with a compressor on a channel that's muted. When you're oversaturated this starts happening repeatedly.