I believe that there has to be some efficiency gain as well. Certainly there would be if you burned without storage by loading up to the gills and then letting it idle.
However, data doesn't generally lie. I haven't seen data from my own (highly instrumented) experience or from anyone else that quantifies a measurable improvement from running a gasifier efficiently without storage, to running it with storage. I'm still a big fan of storage - wouldn't want to give it up, but if you're already minimizing idle time I wouldn't suggest that you cut less firewood based on adding storage ;-)
I think in a nutshell, if cost and space was not an issue I would have storage installed but still plumbed in such a way that I could run the unit in an 'on-demand' mode for those times when I'm not busy and want to be more pro-active with the daily operation of the unit. Kind of like operation of a traditional wood stove.