At least according to Google, there is a wall between paid and organic results, and ad spend has absolutely no effect on organic ranking. I haven't seen any evidence that that isn't true.
However, I will say that if you spend enough on advertising, you at least are likely to have the opportunity to get information from your rep at Google. If something happens to your organic traffic, you may be able to get an idea of what's going on, whereas others will have no choice but to try to figure things out on their own. That's not a lot, but I've been told that it can be helpful in some situations.