The thing is, you don't need warp to conquer the entire galaxy in, say, a million years. Sublight ships with really poor success rate will suffice, if you are motivated enough.
But by that token, successive waves of colonization would probably constantly take place, erasing previous empires in geometrically intriguing patterns, and resulting in a jigsaw puzzle of cultures at varying levels of development, retardation or renaissance. Lacunae and fallows would also inevitably result, even if fairly locally.
In this respect, warp drive would be fundamentally different from any other innovation, as the formidable speed of information propagation would "synchronize" the galaxy and pit fairly evenly matched factions against each other. Basically, we seem to be witnessing the very thing around Earth, with Vulcans, Romulans, Klingons, Andorians and now Earthlings vying for dominance.