I think it relates more to the overall arm action rather than just the down swing part but of the two I think the arm swing up, more specifically, has more of an impact on the extension of the opposite leg. Still it is probably more of a case of the overall action than the isolation of any specific part of the cycle. If you have not checked out that tech. thread, do yourself a favor and do so. Again, I think correct posture permits this extension to occur and without it the complete extension isn’t likely to occur.
Again, this goes back to exactly what I was talking about above. It’s not that the backward action is unimportant, it’s that it happens so quickly the sprinter shouldn’t feel it. If the sprinter feels a significant backward motion he’s probably exaggerating it which is slowing his stride frequency. I made a similar mistake with knee lift and stepping over with the swing leg.
I think if the coach sees that the backward motion is insufficient he might want to cue the athlete, but I would do so by telling the sprinter to drive down harder rather than back. Just my 2 cents.