I have wondered for quite a while what would happen if china continued it technological advance during the Song Dynasty or if a subsequent dynasty, whether Yuan or another potential option, would continue this process and how it would affect China, it's neighbors and the world as a whole?
Obviously it's difficult to say, but we can probably posit the following points:
1) Industrialization will probably be preceded/proceeded by a population explosion in China, which means that the arable land/capita ratio will fall quite drastically - judging from OTL Chinese and European experience, this creates a large pool of dispossessed farmers, which is a particular bane of Chinese dynasties since this class provides perfect fuel for rebellions.
Now you could argue that industrialization can absorb some of this surplus labor, but again the sheer
scale of the Song peasant migration would be unprecedented and even OTL China today doesn't allow 100% free rural-urban movement (the
hukou system prevents access to urban amenities for migrants).
There's also the posited 'high-level equilibrium trap', where such a high level of rural-urban migration pushes the cost of labor so low that no amount of early industrial technology can compete, which in the long-run stifles innovation and prevents sustained industrial progress.
2) Song Dynasty China was quite anti-militaristic. Its founders had learnt from the previous collapse of the Tang Dynasty due to powerful military commanders, and turned the Song military into a pretty weak if numerically-imposing force. Song soldiers were pretty much at the bottom of a rather stratified society, and the Dynasty used every opportunity to consolidate civilian control over the military, even to the extent of appointing civilian co-commanders in the field.
Obviously this creates severe limitations to Song military power, especially considering the growing strength of their increasingly-advanced neighbors such as the Khitan Liao, the Tangut Xi Xia and the Jurchen Jin. Technology isn't going to alleviate the basic problems of poor morale, hobbled leadership and perennial bureaucratic suspicion of military leaders. I doubt an industrialized Song army would perform much better in battle than a pre-industrialized one.
3) Song government was the first true 'bureaucratic' government in China. Previous dynasties had a major aristocratic component to them, especially in the rural areas - but the system was totally wrecked during the turmoil of the Five Dynasties and Ten Kingdoms. Further developments to the examination system also consolidated central control over the entire country. Even imperial power was curtailed in the face of Song bureaucrats. This expansion of the Song bureaucracy was what made large-scale intervention in the Chinese economy possible, such as in Wang Anshi's New Reforms.
However, as with all bureaucracies the Song government was very prone to deadlock. Debates over policy were very common and dramatic new shifts in policy would create disputes that paralyzed the country for years and years: examples include the debates over Wang Anshi's New Reforms and the perennial pro-war/anti-war disputes.
There's also a disturbing tendency for extremism in Song policy - a New Reform government, for example, would abruptly introduce a whole raft of economic and social reforms during its tenure, only for them to all be scrapped when a conservative government returned to power. Rival governments would routinely purge their opponents from all offices, sometimes along with even moderate members of their faction like Su Shi. The Confucian mindset, which judged virtue on how rigidly one followed the precepts of Confucius, could be as intolerant and zealous as any standard religion.
The OTL Song bureaucratic system didn't work too well in dealing with the issues facing the Song Dynasty, and I don't see how it would perform better in an industrialized Song TL, where the social problems facing the dynasty would multiply in intensity many times over.
So
tl;dr - Song Dynasty industrialization probably won't lead to uber-China, and it's even possible that the whole phenomenon eventually just collapses in a haze of economic and social ruin rather than ushering in a sustained era of progress.