The Russian sociopolitical culture is very imperialist, which is no surprise given that the country is one of the few remaining colonial empires in the most traditional sense (i.e. the metropole milking vast occupied territories), and it cannot really exist as a single entity without this kind of politics.
That said, leadership does matter. These kinds of ideas find support in Russian society when they are put front and center, but without someone to actively do that, people just grumble about "them not respecting us as they used to" etc.
At the same time, Putin does not represent the most radical manifestation of this ideology, either. Someone like e.g. Strelkov could truly go all in on "gathering the lands", as Russian historiography usually describes re-occupation.