Not really. You can still get traffic without having a good SERP through social networking, bookmarking,etc. There are various factors that affect SERP. Keyword competition, onpage factors and quality of backlinks are other factors that constitute a site ranking.
Before you can check this, try to check your analytics. Is your traffic is referred from search engine or not? If all your traffic is referred from direct or referral and not from search engine, then we can evaluate this. Traffic from direct or referral does not increase SERP ranking. Only backlinks will do.
well the question can't be just answered in yes or no but one can say that traffic does affect in SERP but we can't just say traffic alone work in SERP traffic with regular content update will surely does affect as it is said that if you will get traffic you will get more people coming to you and among them the one who like your website would like to link with you which would in all affect in SERP and PR both.
How much "traffic" your site gets is NOT a ranking factor that Google or the other engines consider when ranking your URLs for a particular keyword phrase. However, the more people who see your site (especially if it's targeted traffic)... the more likely it is that some of them own a blog or web site and will link to your site IF your site offers some content or tool that they really like and think their visitors will like as well... So indirectly it can help rankings since more traffic "can" lead to more backlinks which IS a ranking factor.
your site can good PR if you are getting more visitiors but for any specific keyword you can's be guaranteed for good ranking
Not traffic alone. However, if people really like your site, they may link to it in their blog or on a forum "hey, you guys should check this out" type of stuff. Traffic alone, won't do anything though. Welcome to SEO!
Traffic does not drive SERPs and Rankings, links, good content, good meta titles and descriptions and keyword placement do.