I know this is the case for registration where you dont want the user to bail. A good example would be creating a map on Google Maps.
Designing for Emotion does into a bit of detail on this (specifically about registration as well); many good sites will cut back "frills" when an important task is at hand.
For instance Carbonnade lays on the fluff and fancy pretty heavily on their opening page; it's meant to entice and be fun. Once you log in much of the extras disappear, and once you're reading someone's portfolio the "fun" bits go away; they would be distracting and even unprofessional.
In addition these extra links and such add to Cognitive Load, which I discuss in detail in this related answer. The more complex your task is the more important cognitive load is; distracting users with extra elements can only have a harmful effect.
Lots of research has been done on distractions and their impact on performance, though often in the context of real-world distractions, but the general result is pretty obvious; distractions harm task performance, especially with complex tasks.
That said, removing navigation isn't always the best idea, a user may want basic navigation to exit the task. Definitely remove ads, read more links, unnecessary junk like that.