I could see it working, but mainly for queries that have one clearly-best result, or where the 'snippet' itself answers the query. So perhaps for 'answers' search more than general web search.
The implicit user feedback created would be great... but uses might be frustrated by not being able to scan many results quickly. (I always set Google to return 100 results...)
(Or similarly, if a forward-thinking group is willing to help train, are their choices representative enough of what the impatient masses eventually want?)
I think it's a promising area for experimentation.
Such an engine has to start small and be trained for a few months, otherwise users will think it sucks. As it grows, it adapts.
I bet one could actually do this very easily using yahoo BOSS. Want to take a stab at it? If anyone wanted to work on this, I'd help, so long it was written in python.
The search engine learns because when the answer is wrong, people select the "next" button. If you just return a list of search results, people will often click the first link because it's first.