I have noticed both, but happiness does seem to improve more after the start of useful work than useful work improves after an increase in happiness. I might describe it as certain types of work requiring a threshold level of happiness to initiate, among other requirements.

I've been noticing this tendency for years and trying to use it to my advantage (much to the annoyance of all the mainstream types who only inquire into my methods when they fail). A particular anecdote that comes to mind is how, after weeks of not managing to care enough to complete any assignments for a course that I like so little as to have since given up on, I discovered HPMoR, which I read in one sitting, other than the ten minutes in the middle where I stopped to complete one of these assignments.

Happiness in / Happiness out, so to speak, except that happiness is obviously not the only activation condition, so attempting to use it without the others present just wastes happiness. (The trouble is how one goes about recognizing the necessary activation conditions for useful work and their presence/absence so as to avoid wasting happiness unnecessarily.)