No the 9mm conversion barrel has the same diameter of the 40cal/357sig barrels so it will fit in the 40cal/357sig slide. However the 40cal/357sig barrel will not fit in a 9mm slide. So the 9mm barrel you have will work in a 27/23/32/33 glocks. It will stick out about 1" in the 27/33 Glocks.
If the 40cal/357sig barrels fit in the 9mm slides there would be no need for conversion barrels you could just buy a stock 9mm glock barrel to switch out caliber's.