99.999% of all commercial loads available now for the 357SIG are actually .355, same size as 9mm.
And Lunde organized a group purchase of 9mm Bar-sto barrels for the SigPro 2340.
I was a happy recipient of one for the mere cost of $166, shipping and all.
9mm ammo loads and feeds fine in the stock mags, and operates the slide just fine.
12 fit in the stock 10 round magazine, and they load easily.
They feed and extract 100%, and why not, my dillon 550 uses the same shell plate for .40, 9mm, and 357SIG.
I would imagine that 9mm would shoot fine through the 357SIG barrel, but the brass would prolly be too stressed to do that repeatedly, and you already have the gun, why not buy the right ammo, or get a conversion barrel?
I would imagine that the brass case wouldn't seal well, and would fail to cycle, but 1 bullet would be in the air, and you would prolly have to fumble around, clearing various jams.
I still wouldn't do it except as a last resort.