It's possible not only that Chinese Government but also other government can block different sites that are related directly to Bitcoin and if the Government want to cut the internet off for public and private use then they could do so. Governments can do whatever they want in their country and manipulate everything to their favor.
It is not easy to ban bitcoin in a certain country. Though there are already countries that have ban btc but users can't stop using btc. And yes it is possible to ban without shutting off the internet but it will take a lot of process.
Actually, it is easy for a Government to do that. Like what I've said Government can manipulate everything. They have total control over this type of case. They could make a law that prohibits citizens to transact or use Bitcoin in the corresponding country.
Ok, How will the Chinese government be able to stop me from "receiving" bitcoins from someone for something I did for them
online? How will they stop me from crossing the border with a piece of paper with a QR code with my private key or sending
those bitcoins to a friend's address in another country? Bitcoin will just go underground, if it is banned in a specific country.
To answer your question logically, Let's say you were written/printed down your QR Code and Private Key to transact over the border. How would you access your wallet if the country bans those Crypto related apps such as Online and offline wallets, this forum and etc.? If you already have the account before the law or ban was implemented then for I think it is safe to say that no one can track it down. But how would you access it? Don't underestimate the power of Government.