[Edit: apparently this is not true. DDG does not use Google, though it does use Bing and some other broad and narrow coverage search engines]
How long would duckduckgo have to grow at its current rate to become an actual blip on Google's radar? On the one hand, you're small. On the other hand, keep up a fast growth rate long enough and you get bigger faster than people's intuitions' expect.
I vehemently disagree. The early web crawlers and indexes did not cost hundreds of millions of dollars to run. Granted, there is significantly less web results than there are today, but the cost you're referring too is the entirety of google's servers. That price tag also includes the cost to host the web traffic of being the number 1 website in the world. You're talking a price tag which is indicative of a final product.
A new search engine would not have those costs initially, and if managed properly from the very beginning, would be able to scale and cover their bills, remaining profitable up until reaching (and hypothetically) replacing google.
I doubt that figure, but even if it is true, you're still talking about a final product (not a new start up). It's a figure that includes things like marketing and insane web traffic. These are things that a new search engine would not have initially.
I'm not saying running a search engine is cheap. It's not. But the implication is that it's like the pharmaceutical industry where you need billions just to get in the game. It's not like that at all. In fact, there have been a few search engines which have tried to get in the game. Search engines like Cuil (anyone remember them?). They may have failed but that doesn't mean it's impossible. And it certainly doesn't take hundreds of millions of dollars to get started.
And you don't need to doubt that figure, Microsoft discloses it in its financial results.