Sure, you CAN do it, but it doesn't seem to work all that well. Another poster here was wondering if the accuracy might be better if you nearly fill up the 38 case with powder as compared to a lot of empty space in the 357 case with the same charge. I mean, you take a look at how much space a "normal" amount of Unique takes up in the 38 case and it sure looks like you have a lot of extra space you could fill up.
It got me to wondering too so I tried it once. The revolver I was using was chambered for 357 and I had shot plenty of stout loads in it so I didn't worry too much about it. And I loaded up a progression of loads too so that I could make sure the pressure wasn't building up too much. You can't just dump the same amount of powder into the 38 case as you would the 357.
So I loaded up a bunch of progressively hotter 38 loads. I didn't have a chronograph so I didn't measure velocities. I don't have the load sheets in front of me here, but suffice to say I had some of them loaded with significantly more powder than called for in the 38 +P loading.
The interesting thing though is that the accuracy did NOT improve as the cases got fuller. The accuracy seemed to stay fairly constant, maybe improving to its best as I got "almost" to the +P level. Then it started falling off as I exceeded the +P levels. The recoil wasn't remarkable, but the hotter loads were just getting worse until I finally quit. The velocity might have been close to the 357 loads but my accuracy using a normal 357 case and load was far superior to the 38 "super hot" loads.
It was a fun experiment, but it just showed me that the powder and ammo makers had this all figured out 70 years ago or so. If you want the best performance in 38 cases, then stick to the standard loads for them. If you want 357 velocity and performance, then use a 357 case.