Yes. I use 38 data for many of my .357 rounds, and yes it does cut down on the circle in the chamber. Watch out for certain powders such as Win 296 though, and watch out for jacketed loads that are too "weenie". I stuck such a round in the barrel of my Marlin rifle, but never had a problem with any of the 4" revolvers that I used the same load in.
One easy method to remove that circle is to push a fired, but unsized .357 Mag case into each chamber. It cuts the worst of the crud out, and makes cleanup a whole lot easier.