Does GoogleAds prevent standard listings?

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I have a client that is paying $12000/mo. for his GoogleAds. He wants us to get him optimized in Google's standard (organic) listings. However, ever since they have gone public, I don't recall ever seeing paying customers also indexing well, or at all for that matter, in the standard listings. He would like to reduce his GoogleAds budget if we can get him to place well in the standard listings for some of his words and phrases he is paying for. We are inclined to not make the attempt if Google is blocking this from happening but cannot find an answer to this. Makes sense. Why lose revenue by allowing their paying clients to index well otherwise. Any feedback on this would be appreciated.