Lets say Google Search algorithm was broken down and somebody writes API's callable to crawl, index and search information.

Note thare are lots of APIs already for crawling the web, in fact there are a few on CPAN. There are also APIs for indexing and search (I quite like Lucy).

Will Google still claim that API's are not copyrightable and its perfectly ok for some one to run a Google search engine clone?

You do realize that there are other search engines out there, and the google does not sue them? Try duckduckgo for example. Or bing. Or yandex (if you happen to like Russian sites), or Baidu (if you happen to like Chinese sites).

If somebody wrote a clone of google search in the sense of using Google's logo on their page, they would infringe trademarks, not copyright on an API.

I think Google also has a patent on their PageRank algorithm, but the API and the ranking algorithm underneath are completely separated.

Anybody would object to a API clone, if that API is the very revenue source of their business.

I don't know a single company that sells API licenses at the core of their business.

Google sells ads on search result pages. Oracle sells software, trademark licenses (so that others can call their java implementations "Java"tm). Sun did too. None of them make money from APIs.