It should. Mine is a 40 sp2022 but it's the same as the 2340. I picked up this 9mm barrel last year when CDNN was dumping them for $99. Of course SIG doesn't recommend the factory barrel conversion or probably installing in the non-lci slide bit it should be fine for range duty. 9mm mags will work fine and in a pinch 40/357 mags will feed 9mm. "Get some"
Some time ago Barsto barrels made a conversion barrel for me to go from 40 to 9mm in my 2022. That barrel is accurate like a darn rifle and it shoots 9mm with very little recoil. I do not think they make them any more for the 2022.