No I am not talking about the google search box incorporated in sites but the site's own search box. Answering your 2nd question, I meant that the URL won't be found via site navigation as it is a dynamic URL that is generated. Awaiting your response on the same.

For example, if I search for an 'x' item in a site's search box and if the site displays a list of results based on the query, would that page be crawled? I am asking this question because this would be a URL that is non existent on the site and hence am confused as to whether Google bots would be able to find it.