So I live in mainland China, under the surveillance of the infamous Great Firewall. However, for my surprise, I am perfectly able to browse in my 3DS' (as long as I don't access a "forbidden" website) and (not so perfectly) access eShop and download games etc. However, it seems to me that some in-game (and maybe others) online features are being blocked by it.
In my case I have a problem with in-game online operations in Pokemon Sun. Every time I try to trade or battle online I get an error, usually error 001-0502 but eventually also error 001-0803. This seem to suggest I might be having a problem when trying to connect to the server. I tried and look for nearly everything that could be googled but nothing really seems to work. So I cannot help but to wonder if this error isn't being caused by the Great Firewall, which is blocking my connection to Nintendo's servers?
Putting the question in a more general form:
How is 3DS' online gaming experience affected by China's Great Firewall?
Best Answer
Error code 001-0502 is a network problem, as stated in the Nintendo website. To solve it, change your 3DS DNS to 8.8.8.8 or 8.8.4.4 or try using a VPN. Also, it appears that you may need China Unicom broadband as a prerequisite (i.e. if you're using the Great Wall Broadband, you're pretty much on your own).
Adding on, apparently the majority of people who get this error are using their school's internet - they have the same conditions as you - able to access the ESHOP etc but not the game's internet. Another recommendation (if the previous paragraph didn't work) is to use the internet from your phone's hotspot.
Most of the error codes starting from 001 (including 001-0803) means that you're (likely) blocked by the firewall and you'll need a VPN to bypass it. (Source)
Answering your general question, most of my Chinese friends use a VPN to do anything on the internet, which includes playing games and accessing Facebook. Likewise goes for 3DS gamers - they need a VPN.