TL;DR: It depends on how much space the melody leaves for responses to fit into.
Given the two songs mentioned, the reason "Autumn Leaves" works and "Days of Wine and Roses" doesn't (rather, doesn't in the same way), is because the "Autumn Leaves" melody leaves more space via its consistent long, sustained notes. In "Days", the spaces between melodic segments are much shorter, so there's less time to interpolate chord "responses".
Here are the first four bars of "Autumn Leaves", with rhythm indicated where chord responses might be placed.
And here are the first four bars of "Days of Wine and Roses", again with melody plus the same rhythm "responses".
Clearly the same response pattern can be made to work with "Days"; however, it operates differently in m. 3, for example, because the response overlaps with the final note in the melodic phrase. This latter "problem" persists were we to continue with "Days".
In the end, whether this "works" or not is purely an aesthetic judgement.
But, the less space in the melody, the more difficult a "call and response" with the rhythm becomes. Take "Donna Lee":
There just isn't room for a rhythmic response between melodic segments, aside from an accent here or there.
A song like "Freddie Freeloader", however, could have all sorts of rhythmic response, because the melody is so open.