In general, this is not well-defined (you could look at the completion of the category by homotopy colimits, I guess, but for some reason I feel like this isn't very useful).  A sheaf on the geometric realization is equivalent to a covering space.  The geometric realization throws out too much data for this sort of thing to be very useful.  You should really read HTT by Lurie, because this is what the book is about ([generalizations of] sheaf toposes on infinty-categories (which are special simplicial sets).  You usually want to look at sheaves of Kan complexes, which are a higher-categorical equivalnt of categories fibered in groupoids.