Do the search requests made by the users influence the Google crawlers "attraction" by this keyword?

Let's say Google has some hits on a specific keyword in the search index. And now I search for exactly this keyword. Will the Google crawlers react to the search and keep looking more intense for pages that could match this keyword?

A reason why this could be important: Privacy when searching yourself. Assume you just want to know how much Google (and thus other people) can find out about you. If now any (statistical) additional search for your name trigger the crawlers even one step harder to find even more about you, it would have the negative effect that you would actually be found easier in the future, even though you had the intention and hope to find out how few Google finds about you.

It's a bit like the dillema in quantum mechanis: Does observing the system automatically change the system?