Yes, coach may use a courtesy runner, but the role of DH is eliminated by pinch running the defensive player (the pitcher in this case) for the DH.
Rule 3-1-4:
Quote:
The role of the designated hitter is terminated for the remainder of the game when:
a. the defensive player, or any previous defensive player for whom the designated hitter batted, subsequently bats, pinch-hits or pinch-runs for the designated hitter
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