If the string was exactly central, and the release was almost mechanically clean with no twist or bias to one side caused by the fingers, the arrow would be pushed out, away from the bow regardless what side it was on. Trouble is, a right handed archer will always twist the string clockwise at release, which works fine for the arrow resting on the knuckle but not the thumb.
A left handed archer faces the identical issue, as they twist the string anticlockwise but the arrow is on the right of the bow, still over the knuckle so it's not a problem.
If the right handed archer shot off the thumb (and wasn't a freak like TMK..) but released the same way, it's probably gonna cause the arrow to fly off as the string twisted, but if it didn't and everything stayed where it was, the arrow would likely behave as a mirror image to one shot off the knuckle. It would point off to the right to start with, the string would force the tail forward and the arrow would bend round the bow, just like the knuckle-shot one.