Liberal Democracy likely can not work in very ethnically divided countries without some common cultural denominators creating an overarching loyalty. You need to get past the tribal/clan based loyalties and that is next to impossible in some societies. But democracy can be established in other forms than the Western liberal version. A federation of clans or tribes could also be a democracy.
Well, I assume a democratic China would have strong ethnic separatist parties in regions like Xinjiang and Tibet.
I wonder what a Chinese election map would look like?
Likely, but they would be too small to sabotage the political process. Seccessionist parties need to reach some size before they're able to do that.