The answer is "yes" of course a Chinese made Patek Philippe would be an object of appreciation. But there isn't one.
There's actually a rich history of Chinese watch making and it's worth reading up on if you're into mechanical watches at all: http://chinesewatchwiki.net/History_of_Chinese_watchmaking
In fact the project 304 chronograph is still considered collectible, even the reissues: http://forums.watchuseek.com/f71/review-ed1963-chinese-milit...
However, back to answer your question precisely, China simply doesn't have an industry or heritage or history that can support a Patek, which is why it doesn't exist. Even with the history I've linked to above, the Swiss industry is light years ahead and it's not even close.
I don't think you should let your bias, if any, of the very inferior counterfeit movements and counterfeit casing industry color your opinion of watches. Anyone in the know would trivially identify the differences. To your analogy it would be like producing a cheap engine and simply calling it an F1 engine. That's not how it works.
Furthermore, if you asked this theoretical Chinese sweatshop to build a modern highly complicated Patek Philippe, it wouldn't cost 1/100 the price, it would cost 100x the price if not more. They'd have to start by sourcing synthetic materials, reinventing tools, or recreating components that a theoretical sweatshop wouldn't even have access to. Part of why counterfeits are so cheap is because they source really cheap Japanese or local Chinese movements that have had decades of build up to scale to the current counterfeit prices. Meanwhile, the real deal modern watch movements are decades more advanced.