No, that would require that you pronate your right hand on the way back. Once you have taken the grip per the video so that you are single axis and you reached full extension & abduction with the right wrist (90° preferably) then simply biceps curl and point your thumb over your right shoulder. This is the face position that is right for you.

Would this be a good check point to ensure no club race rotation assuming one's grip is correct?

More than just the grip would have to be correct. You must make sure that you have no extension of the left wrist that your hand is fully abducted and extended, and that the right arm is in an externally rotated position as well, for correct elbow alignment with the spine. And even if all that is correct it is all for not if you don't make the first move down as I describe.

This is not a good checkpoint to ensure anything except the continuation of golf jargon.

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