I do not know about SE specifically but my experience over 15 visits to China and reports from friends "in country" who I have tried to provide photo access to is that many sites are blocked or significantly affected by the GFWoC. Some that come to mind are GMail, Google, Facebook, Wikipedia, Wikimapia, Fotki, Flickr, ... . Most sites that serve photos.
I have seen Facebook pages created by friends of mine 'in country' but am told they are not meant to access FB and people 'in country' who I have pointed to my FB photo pages have not been able to access them. Skype works well - and allows photo and other file transfers.
D...box has recently introduced albums and so far (as of a few weeks ago) these work.
GMail used to work until a while ago when Google withdrew from China. Best bet is now Google Hong Kong which half works.
I'd not guarantee that Mongolia is any better - but have no direct experience.
An excellent "work around" is to use the free for non-commercial use TeamViewer . This is effectively remote PC access software and you need a tame PC somewhere on the outside to access BUT once loaded you can get full access to anything the remote PC can do. (I transferred files across a home LAN between remote PCs, accessed programs on the remote system and can access any of the above services. Operation can be optimised for speed or display-quality and overall the experience was very pain free after a modest amount of learning. The footprint on the mobile/remote device is small and it will run on a wide variety of platforms.