This afternoon, I've been tinkering with a couple of new sharpeners I picked up recently. One, an EZE-LAP 10" diamond 'steel' (oval) in what they spec as 600 grit diamond (feels a little coarser than DMT's '600' mesh). The other sharpener is a simple little AlOx pocket stone I picked up at Sears a few days ago, for about $2.50. It finishes a little finer than the EZE-LAP diamond rod; I'd guess it approximates something like 800 grit or so.
After testing both of these sharpeners on a cheap Japanese-made paring knife of unknown stainless (it may emulate something like AUS-6), I stropped the edge lightly & for just a handful of passes (< 5 per side) on a 'hard' strop of artist's canvas over basswood (another experiment

), with some Sears #2 grey compound ('Regular Cleaning' for hard metals; I'm sure it's AlOx, but grit size is unknown). This compound is very aggressive, but if used sparingly, really leaves some nice tooth on the edges produced as described above. Both of the sharpeners leave some fairly obvious burrs on the knife tested; this is primarily why I used the strop & compound, as it cleans up burrs very efficiently, and also refines the edge nicely.
In a nutshell, in answering the OP's question, I can definitely see value in stropping a relatively coarse-grit edge, so long as the strop & compound are wisely chosen to truly enhance it with that much more 'sticky bite', instead of just polishing it. It's easy to quickly erase an effective-cutting, nice & toothy edge in pursuit of a pretty & shiny one, if the stropping setup isn't chosen thoughtfully and used sparingly.
David