We assume he wont win olympic gold, right?
I think helping Russia win a best on best tournament would be his preference. Thats a process for years most probably.
Olympic team GM can do less than KHL or FHR (federation) leader. GM deals with grown up players and federation head can force the total cleaning we supposedly need to take next step forward.
I expect us to have a down period (see, there is no one behind Kuzy, Kuch, Tank and Panarin generation, so there will be some grim years right around Ovi retiring).
Thats clearly a possible scenario. Also Putin can directly ask him to do it. Because it'd be hard to find better person for that.
Thats my take.
Also I take into consideration the dynamics for your society. Its already wild enough from Russian POV and becomes more extreme from our traditionalistic standards each year.
10 years from now Moscow will be the capital of the world with 90+% probability (my own estimation, lets say it that way).
So I bet Ovi will be somehow connected with Russian hockey and living in Moscow suburbs.