Yes it does. Just copy setpatch, workbench.library and icon.library from os3.9 to os3.1.
The point was that you can't just copy icon.library.
I did all this years ago and I remember there was something which made me forget it and give up - instead converting 3.9 icons to use in 3.1. (possibly you need the crap picture.datatype, or the setpatch was screwing something up for me... I forget)