The answer to your question is yes. Not only "can" they, but certain services do collect data (I'll update this answer with references when I get a minute).
Further to this, from using Google Analytics I've seen reports on 'from' where a user came to find my site. So, what they searched in Google will be the referring URL to my site. By this logic, if you typed a password, for example, into google, then visited a site with some analytics running from this search, that site could have access to the value you put into the search box too. Bit of an edge case but, still.
As an aside, the title for this is pretty misleading. Nobody would be hijacking your history in the scenario you've described - they'd be capturing data, sure, but nobody would be manipulating or interrogating your search history as such.