Of course it will. Population and money will tell: talent will appear, be funded, and produce. There may of course be some limitations - realistically much Western output didn't significantly touch most of the world either, and there will always be likely to be barriers (language will be a major one). But inevitably China will end up with a cultural output that reflects its general power. Gradually, that cultural output will have its hits, its presence will increase, and become more normalised.English has become dominant primarily also because of soft power like a highly commercial popular culture(espescially songs and movies) that is exported wordwide. I don't see China ever exporting something to a similar extent.
Wrong. Lingua francas no more survive forever than empires do.Power alone is not enough you need something that resonates among people and American popular culture is still unmatched in that regard. The world is also largely homogenized in terms of international business and economics. You need a language that everyone involved is atleast somewhat literate in not a language that is only useful for native speakers. Even in China's sphere of influence english will remain dominant for the simple fact that communication is otherwise impossible.
Curious fact: in 1815, when Wellington met Blucher during the 100 days campaign, the language they spoke to each other was French, because Blucher did not understand English and Wellington did not understand German, but pretty much every one of the upper classes from Moscow to Lisbon spoke French. Europe - the UK included - already had a lingua franca in the early modern era and it was French. And yet it eventually became English. Latin died as lingua franca in Western Europe. Arabic supplanted Greek across the Eastern Med.
As countries increasingly do business with China, it will become expedient for them to learn Chinese. As countries take in newly affluent Chinese tourists, they'll start to learn Chinese, and as they visit China for tourism in return. Businesspeople will learn Chinese to impress, bond with, better understand the goings on of the major economic power. Chinese cultural output will gradually inspire more and more people to learn Chinese to enjoy it. These factors will lead countries to institute Chinese as an official language for schoolchildren to learn, because of its utility. In the Far East, the benefit of learning Chinese will grow and become a lingua franca alongside English, and eventually a tipping point will be reached where the benefits surpass that of learning English, and when it does English will be mostly swept away. It may take 100 years even more, but unless China has some sort of major setback, it will happen. Then the same "contest" will begin to occur at a global level as it had at a regional level in the Far East.