As in the case of the Maya and meso America, yes the multidecadal drought did end, but the society collapsed before it ended. That's the point. I don't think anyone says global warming is going to destroy the planet, but it sure can do a number on our societies. How long do you think we'd survive as a nation if, say, the population of southern California had to relocate somewhere else? That's going to be an immeasurable cost. I can conceive of that, alone, dealing a major blow to American society. Then add in increases in superstorms on the East Coast and you have a perfect storm of disasters.
Well, first, we have an example of that in the 20th century. Global warming started sometime in the late 19th century but in the 1940's with the advent of WWII suddenly industrialization jumped many fold. It caused a huge amount of sulfate aerosols to be pumped into the atmosphere and caused cooling. From the 1940's to the 1970's we saw cooling. This was because we had put a negative forcing in (in the form of pollution) that offset the warming forcings like greenhouse gas emissions. When we cleaned up the air in the 1970's the warming started in again.
If the temperature "leveled out" it would have to be because some negative forcing offset the warming forcings we are currently doing.