Okay, I didn't see this thread until now, but I still don't believe this premise would work, and I don't care if I'm called a SJW (been there done that). The idea that just because a marriage occurs with an Asian person means that all of China will somehow roll onto their backs to become submissive, subservient slaves of a foreign royal family is completely wrong and actually perpetuates a stereotype.
1. As
@Admiral Matt just said, Aisin Goro isn't even Han. If a Manchu dynasty wasn't Han enough for the Han, why do you think a half-white, half-Manchu dynasty will somehow be more than enough?
2. Starting in 1734? At that time, China was not about to be beaten by the British or any other European power.
3. "The West" rules China? Sorry, but they can't really agree on anything regarding colonization, especially in Asia (and not just Asia). They were more likely to steal trading posts from each other (East Indies, etc) than from Asian countries. Furthermore, this assumes that the Qing have no ability to actually play some minute level of politics and play off the many European colonizer against each other.
4. White men. Wow. I have no problem with them, but saying that white men would intermarry with other races at a time like this is pretty strange if they had other options, like bringing their families over. Of course, some of them would, but it would more likely be non-consensual, since even in Hong Kong under British rule, Han women who intermarried with the British were looked down upon and in the lower parts of society. In order to "intermarry with the elites" as you propose, something's gotta happen, and it's definitely not consensual.
5. Point 4, but differently. I'm not sure if you've noticed, but China is 99.99% Asian (probably a lot more than that, like 99.9999% or something). Maybe you're not aware, but this is perpetuating the same tropes and done stereotypes that can be seen when Matt Damon is the protagonist in "The Great Wall". PS: not going to watch that movie.
6. How does this happen? Do the British capture Qing women? That's non-consensual. If the Qing hand them over as hostages (already unlikely), then they're not even a matter of significance to the Qing dynasty. Making a "hybrid dynasty" does nothing to solve the issue of making these matches happen in the first place.
7. Why would the British and other Western nations royalties mix to form a "new hybrid race dynasty"? There's no motivation to do so.
8. How will there be enough white men to be the ruling class of China? Do they even all want to live and stay in China?
9. Why do they have to be the ruling class? Perhaps you haven't noticed, but there's this nice little trend where Chinese ruling classes all end up Chinese. It's called Sinicization. All those who resist are overthrown... eventually.
10. How do they take over? Divide and conquer? Sorry, the Qing dynasty is really strong and united at this time. Just trying to take over everything? Sorry, China's a big place. Attempting an attempt similar to India? Sorry, China isn't India.
11. Sorry if I sound really aggressive and rude, but this has honestly been tried and tried again by many authors on this board, and I always get really triggered when people add it to a timeline that's extremely accurate with regards to Western history and extremely inaccurate when it comes to the East. But finally, I don't see why the conquerors have to be white males. I honestly don't. It's one of the least likely possibilities. You might as well suggest arming Koreans with guns to take over China, and that'd be more of a possibility than this, considering their proximity, population, and power; plus, it'd be really interesting to see a hybrid Korean-Chinese culture. (P.S. Chinese isn't a race, and neither is Han. It's a culture. Asian is a race, however.) Or a Japanese-Chinese culture. Or a Mongolian-Chinese culture. Or a Vietnamese one. Or a Thai one. And in the end, those are all just as likely as this one.
I'm partly really annoyed because this is an AH with a biracial society consisting of a race that is heavily fetishized and exploited, which literally increases the exploitation and turns the fetishizarion into a fad among white men who will somehow migrate over to China just to have kids with some random Manchu women. I'm sorry, but this just doesn't make sense to me.
P.S. Sorry for the long rant, but these are honestly major social issues that exist worldwide today, and I'm sorry if anything I said offended anyone. I generally avoid some threads that really frustrate me. Oops.