Yes. I was also told by a friend that a simple barrel change will convert a 33 to a 27 and vice versa.
That is correct. I have converted several of my guns from .40S&W to .357Sig in that manner. One other benefit of the .357Sig cartridge is that it tends to make feeding that necked down cartridge into a chamber VERY reliable. So feeding jams are really rather rare in a gun that shoots this caliber.