I have no experience with the .357 sig, but I do with going down to 9mm.
I was able to install and shoot a LW 40/9 conversion barrel made for the model 23 into a smaller 27. It sticks out about an inch, but shoots great.
Seems it would work with the .357 conversion if you made sure the barrel was at least as long or longer than the stock 23 barrel. I know I've seen Youtube videos of guys using extra long barrels in 10mm Glocks for hunting.