@Temstar I wasn't at all making an implication both implicit or explicit that you are or have separatist leanings. I tagged you in my post to gain your invaluable insights to this issue that's all. My apologies for making it seem like I was doing the opposite.No I don't have any separatist leanings, whatever gave you that idea?
People have been wanting to carve out their own slice of China since time immemorial, there's even a relatively successful one over in Taiwan as we speak. Generally though it's one thing to say "the emperor is doing a bad job, signs from the heavens say he's lost the mandate of heaven, follow me and rise up and we'll overthrow him and create another dynasty" vs "we'll split apart China and create a new country over this part of the land".
Chinese people will support the first case if the going is hard, since your intention isn't against China herself but the ruling dynasty. In modern day terminology this type of movement once created would be called "武装割据政权". Wei, Shu, Han from Three Kingdoms, Taiping Heavenly Kingdom and ROC of today are all examples of 武装割据政权. A critically important aspect of legitimacy for a 武装割据政权 is you must claim your eventual goal is to reunify China in totality under your rule. If you win you'll become the new dynasty, if you lose you become bandits. But Chinese people won't begrudge you for trying, the worst they'll do is call you a 枭雄 (villainous hero) as we do for people like Cao Cao. If multiple such 武装割据政权 fight it out over a divided period in Chinese history people would even write epic novels about it later on and refer to the period as one of the many warring state periods in Chinese history.
Chinese people would be very much against the second type. When a 武装割据政权 gives up the goal (or never had to start with) of reunifying China under its banner than this movement transitions to a "伪政权". Examples of 伪政权 are Wang Jingwei regime, Manchukuo and if ROC of today where to transition to a Republic of Taiwan. 伪政权 are universally hated by Chinese.
This trend in Chinese thinking is called 大一统思想 and is fundamental in Chinese identity, has been since the days of Qinshihuang if not Zhou Dynasty. It's very unlikely to go away.
So these separatist that west support would never mount to anything, even if China were in a warring state period because they are fundamentally 伪政权 and not 武装割据政权. It's also why even today ROC dare not change their constitution to make themselves "ROT", even though their claim to wanting to reunite China under Three Principles of the People is lip service at best.
I tagged Chongqing and he's the one I feel who maybe harbour some separatist inclinations based on my cursory readings of his posts.