Iíve recently tried to determine whether stropping will improve the edge quality I can achieve using diamond paste on cast iron. In my first test I took an edge sharpened with 1 micron diamond on cast iron (my usual choice for everyday sharpening) and first stropped it on a boxwood lap charged with 1/4 micron diamond, then stropped it on uncharged leather.
The boxwood and diamond improved the perceived sharpness of the blade (no thread-cutting tests on this one) and subsequent stropping on plain leather seemed to degrade the edge somewhat. The changes can be seen below. Click on the image for the full-sized version.