I've been looking around for gelatin test data on .38 spl 200 grain loads.... can't find any.
Evan Marshall's book "Street Stoppers" includes data for various .38 loads, from 49 grains up to 158 grains. The Federal 158-gr RNL at 755 fps had the best penetration of the bunch - 28 inches in gelatin.
If a 200-grainer did not tumble on impact, it might penetrate that far, maybe even a little farther.
However, if it tumbled (as they're prone to do) the penetration may only be half that distance.
If penetration is your main concern, it might be wise to stick with the 158-gr RNL.... 28 inches is impressive, the ammo is readily available, and recoil would be reduced.