Here's the technical aspects:
The 9mm is rimless, so people say "full moon clips" but that won't work. Any revolver designed to fire with full moon clips has a "shorter" cylinder, on the back end. This allows clearance for the clip and the rest of the cartridge. The clip fits to the extraction groove on the case, so you have to have the case sticking out the back end of the cylinder so you can clearly see the groove. That's too far out for most .357s(all mine at least) to close.
I suppose my .357s have tight chambers or something, as I can't get 9mm into them, they hang up. That's with several guns, by several different makers. I suppose I could force them in there with something, but it doesn't sound like a great idea to me. .380s will fit, so I assume it's the way the longer 9mm sits in a .357 chamber. For me at least it will not work.
Ruger used to make a 9mm revolver based on the Speed-six/Service-six. This used half-moon clips and the cylinder was shorter than on their .38/.357 guns. Alot of people have thought their offering of this caliber ment you could just shoot 9mm in a .357 Ruger, and it has casued confusion. I've had folks swear up and down that I could shoot 9mm in my Speed-six with moon clips until I hand them the gun and six 9mm rounds and say "Show me". They could never get the rounds in the chamber, let alone the cylinder closed with the cases sticking that far out.
I own a S&W 547 which is designed to shoot 9mm without clips. It uses a special extractor star that has fingers that pop out when you push the rod. It's way cool, shoots perfect to aim with fixed sights, and the short little 9mil cases clear the chambers fast on extraction. I even have speedloaders for it.
If you can get your 9mm to fit in your chamber, it should work. It can be done on some guns, I've seen it fit(not fired). Just none of mine. You will need to use a pencil or something to poke them out. A big problem is that when the hammer drops, it may cause the case to move forward instead of setting it off. There is no way for the 9mm case to maintain position, as it headspaces off the case mounth. If it's a tight enough fit, it may work.
I suppose I ought to say that I don't recommend shooting a gun with ammunition not specifically designed for it. Having said that, I've shot 9mmLargo, .38ACP(same case as .38 Super but lower power), 9mmLuger, and .380 out of my Astra 400, loaded in the SAME MAGAZINE. The gun functioned all the way through the mag and shot every round downrange. There's a bunch of other rounds that will fit in there, but those are the only ones I had.
If you try to shoot 9mm out of your .357, let us know how you did.
Ross