We would witness allopatric speciation in cryptos.
If Putin is successful we would see a hard fork based on network access between the Russian blockchain and the rest of the world. Each fork would function as an individual currency with a different exchange rate relative to its usefulness. I imagine that, should this occur, BTC's popularity/market valuation in Russia would be overtaken by an altcoin because:
A) In order to preserve wealth, aka transactions, after Russia is inevitably reconnected to the internet, Russian Bitcoin developers (do these even exist?) would have to distribute a version of the core that would refuse to acknowledge the longer blockchain the rest of the world will have at that time. After the event Russia would likely be left with a national RuBitcoin and an international Bitcoin (the "real" one), each with different exchange rates.
B) Putin could likely put measures in place to prevent Bitcoin-like entities from existing, so a specialized altcoin might likely be more resistant to attack. Also does Russia even have Bitcoin devs? They probably have a few Altcoins. Everyone does.
An event like this would demonstrate a fine form of evolution in the crypto market, I am sure. However this is working under the assumption that Russia would run a national intranet rather than shut down communications altogether. Then again, who can predict Putin? WWIII or bust.