When we talk about search engine's internal policies, it is important to understand two important points:
1. Search engines do not disclose their algorithms used to compute rankings. We are making guesses. Those guesses are educated based on experience and shared knowledge, but these are not absolute truths.
2. Each search engine can operate differently with respect to any specific criteria.
With the above in mind, I am not aware of any direct means by which traffic alone affects search ranking. A page's traffic can indirectly affect the ranking in many ways:
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a user may visit your site once via PPC, then perform a search to find your site in the future and select your site from SERPs. This information can influence ranking.
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a user may visit your site then mention it in social bookmarking, email or other means which can influence rankings
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a landing page is often highly optimized to receive traffic for a given keyword or phrase. It makes sense it would perform well in SERPs for the given keyword. In a perfect world, you can offer an optimized landing page for each keyword. If you offered a site selling Ford Mustangs and you chose to run a PPC campaign targeting "Camaro" and "Camaros", the landing page would likely be a page comparing Camaros vs Mustangs. If the page offered good content, it would likely perform well in SERPs.
Does the traffic from PPC actually have any effect on SEO rankings?
Google has clearly stated PPC does not have any direct effect on rankings. There are numerous potential indirect means by which PPC can have a positive effect on SEO
If we were to create a page that was to act solely as an SEO landing page, would google take note if there was no traffic?
If by "take note" you mean would the page get indexed, the answer is yes. The page can even perform very well in SERPs for a long tail phrase.
Would simply linking from our main site to the landing page be enough to give it a bit of authority, in which we can build upon?
Yes. Links to a page add to the page's authority. Your phrasing of "link from our main site" causes me to believe the landing page is not on your main site. If your landing page is a micro site, generally the idea is to build traffic for your main site, therefore I would recommend linking from the microsite to the main site, not the other way around.
Also, if the main site and microsite are hosted with the same company, or use a common design, the value of any links between them are minimized.