Yes, there is. If the last turn is a quarter turn, replace it by a half turn and a quarter turn in the other direction. If it is a half turn, replace it by two quarter turns.
The set of possible configurations would split in an even and an odd set, so there would be configurations that can’t be solved in God’s number of moves.
(AFAIK, we don’t know God’s number if we count moves that way. I would guess it’s larger than 20)