A cynic might reply that if it could survive Mr Boris Yeltsin, it can survive anything; or that indeed Russian democracy at present is not much to speak of in any case. For democracy of course is not simply - as too many Western spokesmen and commentators have taken it to be - the holding of ostensibly free elections.
Democracy as now understood in the West requires that at some stage those elections should provide a change in the groups holding power. It also demands that the institutions of state power should operate in a more-or-less democratic fashion, and should be backed up by effective, democratically controlled judicial and other institutions. Russia is still far away from this - but then so too are many other states we are prepared to accept as "democratic".
Concerning Mr Putin, there are two more immediate questions: Firstly, to what extent is he his own man? And if he is his own man, what kind of man is he?
The first is of key importance because for much of the 1990s, Russia has been plundered by semi-criminal financial magnates, the so-called "oligarchs", in alliance with senior members of the Yeltsin regime. Their dominance, especially over the sectors of banking and the extraction of raw materials for export, had cost the state immense revenues.
Perhaps more importantly, it has also played a critical role in preventing the emergence of a working free market, and in discouraging the foreign investment that Russia so desperately needs.
Mr Putin has clearly been chosen to succeed Mr Yeltsin, with the approval of the Yeltsin "Family" and its business associates. Without question, he has promised to protect the Family from future prosecution for corruption. But he does not appear to be the personal choice of Mr Boris Berezovsky or Mr Roman Abramovich, the most important financial figures linked to the Kremlin. This fact, and his youth, gives some hope that he will be a much more independent and effective economic leader than the jaded, decayed Mr Yeltsin, let alone Yeltsin's various prime ministers. In St Petersburg, where he was Deputy Mayor, Mr Putin had a reputation for relative personal honesty.
However, he also had a reputation for considerable ruthlessness, as befits his background in the KGB. And there's the rub. However understandable Russian anger with the various threats emanating from Chechnya over the past two years may be, the ruthless conduct of the campaign there is not an encouraging sign for Mr Putin's conduct of his presidency.
Mr Putin's independence and effectiveness are liable to derive to a considerable extent from his security background and his personal grip on the security services.
This obviously presents real dangers for Russian democracy, since it seems to me highly unlikely that Mr Putin, any more than Mr Yeltsin or so many other rulers around the world, will ever surrender power to an opposition figure or party.
On the other hand, it may well be impossible to create an effective state in Russia by purely democratic methods; and as now recognised by Mr Robert Skidelsky and other "conservative" free market thinkers, a limited but effective state is absolutely necessary if the conditions for a working free market are to be created.
Somehow, the power of the oligarchs and of organised crime has to be curbed, and a measure of discipline and honestly restored to the state service and in particular the tax authorities.
So when Mr Putin speaks of the need for a stronger state, he is reflecting not just the Russian tradition but also Russian realities.
In terms of his professed beliefs and aims, Mr Putin's statements so far give grounds for a measure of hope. In his longest written statement since becoming President, he has declared the need for a strong state, which he says is part of the Russian tradition. He does not give much space to democracy, and there is an ominous-sounding warning against partisanship and against what he calls "civil accord" being disturbed in the course of election campaigns.
However, he firmly eschews any desire for an official state ideology, condemns totalitarianism, and speaks of Russian attachment to "universal human values"; admittedly, these words have been found on the lips of many a dictator. He speaks of positive patriotism, "free of tints of nationalist conceits and imperial ambitions". This reflects the extremely unideological mood of the great majority of younger Russians. Mr Putin, remember, is only 47 years old.
On the economy, what he says about the need for a state-led investment strategy in manufacturing industry coupled with strong encouragement of foreign investment sound sensible enough in itself. But it has been said by several prime ministers before him, with very little effect.
At present, the relative health of the Russian economy, the source of some of at least of Mr Putin's popularity, is derived above all from a mixture of high oil prices and the relative weakness of the rouble.
When it comes to really reforming the Russian economy, Mr Putin will be limited by the weakness and corruption of the Russian central state, and by the relative strength of the provincial governors and elites. On the brighter side, however, this will also make it very difficult for him to create an effective authoritarian state covering the whole of Russia. The Kremlin will grow stronger, and local rulers will have to make more compromises, but they will also retain a great deal of power.
I would therefore envisage an interlocking set of semi-authoritarian, semi-democratic regimes dividing power between themselves, with a central state which is strong in some areas and weak in others, and less corrupt than today, but still very corrupt.
The economy will improve enough to reconcile most of the population to the new order. without leading to Russia becoming a new South Korea. Democracy will be largely a matter of rhetoric, but so too will be militant nationalism.
If this is how a Putin presidency turns out, Russia will not be a very attractive sight - but it might be a lot worse.
Anatol Lieven is an expert on Russia at the Institute for Strategic Studies in London.
The full text of Mr Putin's policy statement, with links to the Russian government's website, is available on The Irish Times website, www.ireland.com