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Searching for a keyword would normally have no effect - or even association - with the websites that the search finds, or their ranking.
Even an automated search would not affect the websites, though it may have an effect on your freedom to use the search - you might find your self blocked if you abuse the search facility.
The one exception to all this is Alexa, where using their facilities can promote your site in their rankings. This abuse routinely occurs, with utterly useless sites being given wildly unrealistic ranks; which is why few people who know Alexa give their rankings the time of day.
What will hurt you is doing it for a site that deserves to be punished to begin with. That is to say, such an automated technique could raise flags and put your site under human review. Yes, Google does in fact have thousands of human content reviewers specifically to find spam, and yes, they are most definitely given sites to review that were flagged (in various ways).
Does that answer your question?