Yes there is. A lot of Google's advertising business is selling ads on other people's sites, and they use the information from their search engine to target that; they could run the ad business without it (using data from Google Analytics and elsewhere) - after all it ran as an independent business when Doubleclick owned it.

My understanding is that if search and ads were separate businesses and ads paid search for search result ads at market rates then search would not be profitable (similarly for e.g. Gmail). (In reality if search were an independent company then it might be able to be profitable by selling information to ads in addition to direct advertising revenue - OTOH the legal barriers to selling information to a third party might make that impractical, whereas conveniently they're not an issue while Google remains a single company)