I was wondering if anyone had any actual statistics on this. I was curious if having a video on a website makes an exceptional difference to the quality of traffic coming to the site.
Just having a video in-and-of itself isn't going to deliver quality traffic as you don't hear people saying, "I feel the need to watch a video. I don't care what video or how it good it is. It just has to be a video". So if your goal is to attract "quality" users you should post "quality" content and that includes videos. If you can produce quality videos that your users would find useful/entertaining (depending on what your site is about) you will give users a reason to stay on your site and come back in the future. If the videos are not useful/entertaining you'll encourage users to leave your site and they'll be less likely to come back.
There are lots of different types of videos that can yield different results, for example a viral video, might generate a lot of traffic and even repeat visitor as they show their friends, but they won't be loyal visitors or even high converting visitors. On the other hand if you're doing an in depth series such as how to do X and have parts 1-10 each posted a week apart, if it's useful people will want to subscribe and visit your site often as a reference.
These are just two examples of uses for videos, there are many more. So the short answer is that it can but it doesn't always.
Having rich content increases the quality of traffic coming to a site. It's got nothing to do with a specific technology or content type. Arbitrarily adding a video to your site for the sake of having a video is not going to do anything for your site except slow down the performance. In fact, that sort of thinking is indicative of a get-rich-quick mindset that is not conducive to running a successful website.