Technically--yes, there is a tradeoff in "defocusing". It's interesting to me though that screendoor as an inherent problem with projectors is especially dependent on focus. In other terms, an image from a DVD or even an HDTV feed is less susceptible to defocusing than screendoor. Put yet another way...I find that I can only bring any given image into a certain degree of focus, whereas I can always bring screendoor into perfect focus.
Probably another major factor in all of this is the fact that screendoor effect is a static effect, as if it were a static image. Movies images on the other hand are always in motion. Maybe sharp focus is not as necessary or crucial to moving images, and defocusing stands to affect screendoor more dramatically.