Google search is not only ad-supported, it is also ad-supporting. it is carefully designed to collect and track your every click to feed their advertising business.

I suppose google search business model in a post-adwords world could also be "we have enough cash to run this service until everyone currently alive is dead".

In the event of google search disappearing, affected people would use other search engines and it would make room for better search engines to emerge which is hardly possible right now as google owns the market.