I have been into SEO for about 8 years and am good at SEO.
CTR really does affect Google ranking. Google in past has denied use of Google Analytical's data for ranking sites. But I am sure, it is using the data to rank websites.
How CTR affects ?
I am into PHP programming & Linux server administration too.
Whenever I search for PHP problems or Linux server problems in Google, google mostly throws stackexchange website in the first page for my result.
Sometime, other websites occupies the first 2 ~ 3 positions. I ignore sites which are ranked in #1 & #2 and i directly click on the #3r or #4th link which is one of the stack exchange website.
So in this case, Goolge engine understands that, I prefer the stack exchange website or I get better result my queries in stack exchange.
So, It improves the CTR for stack exchange and places SE sites in the top in few weeks. (It does not happen in a day or a week, it might take few months for Google to learn it).
I search for "my PHP coding issue" in Google, assume I don't get any stack exchange website in the top, then rephrase my query as "my PHP coding issue stackexchange".
So, Google engine can learn in few months that, Stack exchange is having a good stuff, that's why many people want to go there. This also improves the CTR for SE sites.
Similar to this 2 cases, there are many cases, Which I am 100% sure, helps to rank better.
In the above scenario, Google analytic's data not required. But Google uses GA data to find the best sites & best pages for each query.