It depends who does the deposing and what calculations they make about their future health, wealth and prosperity. Whilst it's hard to be optimistic about Russia it's not impossible that they may look at Ukraine and the progress they've made since independence (which even the thickest Russian can't help noticing) and think that they've tried the Soviet nonsense and failed, they've tried Putin style Nazism and failed maybe they should try liberal democracy.When / if Putin goes it will probably be through internal coup d'etat led by disaffected generals. This could easily happen next year. Don't expect an outbreak of liberal democracy in Mother Russia anytime soon.
Oh - and it might be wise not to make any more cuts in the services.
Edited to add:
Also who ever does the deposing may calculate that in order for their coup to be legit they need a 'democratic' leader - some one like Navalney. He ain't perfect but he may be their best bet.