Yes they would, if that was the only thing changed. But we should consider that in reality the cage will rotate with each shift. Additional variables are present as well: variations in cage shapes and in how much the chain lengths are changed to accommodate the added pulley diameter. I think it would be hard to go from a general and isolated statement to an accurate real-world prediction. One would need to do some math to make a strong prediction.

But simply moving the sprocket teeth closer to the pulley teeth, yes that would reduce free length and make it easier for the "next sprocket" to pick up the chain and complete a shift. It reduces the amount of overshift needed, in case any was needed.