I don't think that that weight matters as much as some people think (ie: the endless pursuit of that 15 kg lighter stem) but there is a significant difference between climbing on my old 28 pound touring bike and my 17.5 pound road bike. On flat roads they would cuise at about the same speed, although acceleration and climbing on the old bike is a different story.
"A fast bike on flat roads is about rigidity and aerodynamics, not weight." The key word here is flat.