How is 3DS' online gaming experience affected by China's Great Firewall?

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?
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Images: Eren Li, Bruno Bueno, Eren Li, Eren Li