PPC can save you months of investment in time, effort and marketing service provider fees, by allowing you to test your theories about which keywords are worth pursuing. You can pay Google, run some ads targeting your theory keywords, test your landing pages, refine your adverts (title and meta description in the organic world), establish what offers pull the hardest....
So, in that respect, PPC speeds up gains for organic seo rankings, giving you a flying start on the meta optimisation and page content for conversion rate optimisation as well.
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Unless they've hidden it really well, Google doesn't give you an organic SEO quality score so you know how well you're hitting the mark, but if you cough up a few quid, they will do just that under the label of Adwords.
PPC drives organic on-page optimisation which influences rankings.
Sure, I can't say definitely that if you spend X per month on Adwords, you'll rank Y positions higher organically. But I can say that if you use the tools they give you, you have the opportunity to quickly rank higher organically, convert at a better rate and profit as a result.