You can create free website on blogger, WordPress, wix, etc. Can a free hosted website really beat a self hosted website. If it does, what's the point of spending money on a self hosted website? If it doesn't why these free hosting services exist?
Yes, If your website is receiving a lot of traffic, it sends positive signals to search algorithm. You you get many visitors, it indicates that your content is popular, and search engine algorithm favors popular content.Is traffic in your existing website also a ranking factor? If it is I think a free hosted website will have a really hard time ranking on search engines as it is quite difficult to get traffic on free websites.