My answer is "No".
Now, you will get replies telling you that you can do it. Hell, you can ride an elephant to the local K-Mart, also.
The two cases are totally different.
.38 S&W:
Rim dimeter - .440"
Base diameter - .3856"
Mouth diameter - .3855"
Most common bullet diameter (lead) - .361"
.38 Special
Rim diameter - .440"
Base diameter - .379"
Mouth diameter - .379"
Most common bullet diameter (lead) - .359"