Yes, especially outside of the west first. By transitioning to CBDCs just like how China has done. There are CBDC trials that use the cryptocurrency technology, even in Ukraine by Stellar Network [0] and Bhutan for XRPL [1] to power it.
Probably Russia will introduce their own digital currency that they can control.
[0] https://www.coindesk.com/policy/2021/12/14/ukraine-commercia...
[1] https://ripple.com/insights/bhutan-advances-financial-inclus...
To understand why, we need to make a key distinction between two aspects of the crypto world: (a) cryptocurrencies themselves, (b) on/off-ramps and centralized services that make cryptocurrency easier to access.
(a) Cryptocurrencies themselves
These are very difficult to regulate and shut down. As a government, you can try, but the decentralized nature means that as long as there are _some_ people that want to keep the decentralized network going, it is likely to live on. Hiding a private key is very easy (you could even hide it in your mind!). It's also extremely difficult to prevent peer-to-peer trading. If I want to trade X ethereum for a car, how can you stop me? Preventing that trade is equivalent to shutting down the internet and/or preventing all current cash trades.
(b) Centralized services and on/off ramps
These are very easy to regulate and shut down! This is why there will be short term pain. The best tool governments have right now is to prevent people from ever entering the crypto ecosystem in the first place. If I was a Russian citizen wanting to protect my savings, I would try to move everything into USDC or even BTC/ETH as quickly as possible. If you use a centralized on-ramp and fail to take privacy steps (e.g. for Eth, using a mixer such as Tornado), then this is very traceable. Your best bet is to perform a peer-to-peer trade, but unfortunately if you're holding Rubles right now, very few people would want to be on the other side of that trade.
Once the sanctions begin to bite and the rest of the world assesses the impact, I believe more people will begin to hold cryptocurrencies. Again, the best tool governments have is preventing you from ever entering the crypto ecosystem. Once you are in, and take the necessary steps to preserve privacy, there is little they can do to prevent you from performing peer-to-peer transactions. Sure, the current crypto ecosystem sucks for small transactions. You would not want to buy a loaf of bread with BTC/ETH any time soon (even on the lightning network or ETH L2s, they're not ready yet). However, if you're living in a highly sanctioned state with a crumbling currency and you need to make a life-defining transaction (e.g. buy a car to drive across the border) then what is your best bet? It's cryptocurrency.
https://www.step.org/industry-news/fca-extends-uk-crypto-ass...
Or perhaps not, who knows?