It's very hard to isolate any single ranking factor and attribute specific traffic increases to it, but overall what we know about load speed and Google ranking

It's very hard to isolate any single ranking factor and attribute specific traffic increases to it, but overall what we know about load speed and Google rankings strongly implies a correlation there. Moreover, Google has come out and said it's a factor. Not that we can always trust everything Google says, but in this case it aligns well with their efforts to optimise crawl efficiency. Faster loading websites means more efficient crawling, which helps Google. And if Google recommends something it benefits from itself, it's a safe bet to assume it actually benefits your website's visibility in Google's search results as well. Google is, after all, very adept at the carrot & stick approach to making webmasters do what it wants them to.