Yes, it seems it would open up some options. You wouldn't have to burn a pitcher to come in for one or two batters, or you wouldn't need to burn a pinch hitter if he was on the bench. In theory, he could come up to bat & then go out & pitch.
Pitcher Don Drysdale for Dodgers hit 29 home runs in his career and one year batted .331 with 7 home runs.
Did you hear him say between innings he was “warming up in centerfield with the left fielder, working on his pitches”? If he starts an inning in center and comes in to pitch THAT inning, no bullpen warming up. That, I have never seen happen with a serious pitcher in a critical situation.