Assuming that the bitcoin network spreads to China, and at some point China decides to block all bitcoin traffic through the great firewall, one will end up with a completely independent bitcoin network operating inside china that will be isolated from the outside world by the great firewall. As the bitcoin network is decentralized, the two resulting networks will continue to function, and each will continue to add new transactions to their own blockchain, which will share the history up to the split, but will diverge afterwards.

Now, suppose that after 2 years, a person in China succeeds in smuggling his bitcoins outside of the firewall either by storing his wallet.dat in a tiny flash drive, or by memorizing it in his brain and leaving the country. Will that person then be able to spend his bitcoins by connecting to the network in the outside world? Will his wallet.dat be still considered valid? His wallet will probably now contain transactions that have never been seen in the outside world.

That may be so, but for the sake of argument assume that it isn't.

If the bitcoin network splits into two disconnected components, and their blockchains evolve independently of each other, can they be merged back together once the two components are reconnected, or do the two networks become incompatible?

Any coins older than the split will be 100% fine. Transactions based on transactions that the longer chain doesn't have will not work, at least until those dependencies also work through. Any transactions based on double spends won't work ever unless China's chain ended up longer, then the transactions on the other side that depended on them would disappear. I'm pretty sure I have that all right, someone please verify.

Pretty much the worst split would be a long term close to even split. Thankfully that is the most unlikely of all because any one node connecting to both sides, each of which would be huge will make the transactions flow again.