Does quick defrag and folder defrag help full defrag?

Say I do a full defrag every month. If in between I do a couple of 'quick, 'folder' and 'free space' defrags, will the subsequent full defrag time be lessened?

Or will it move the clusters that have been quick/folder defragged anyway, in an effort to optimise the drive more fully?

This might be a difficult question, because you'd need to know how the algorithms differ and interact with each other.