Google's search engine predates the ads by quite a few years, actually. You'd be correct to say, "without those ads, Google would necessarily look very different than how it does today," but then, that's nearly a vacuous statement.
True, but it's constantly evolving, the technology as we know it today would have been given nowhere near the resources without a large source of income attached. Given that as it stands it is an arms race with ever evolving SEO strategies I don't think it's to big of a leap to suggest that Google Search without the resources it has would be less equipped to keep up.