No it wouldn't. Your ISP still can track your steps. Not to mention, your IP is displayed for the world to see. This means that anyone could get to your computer and get some information, which also displays your location. Not to mention, websites can track your location and use that information and sell it to 3rd parties, jsut like your ISP could. Also, if the website you are visiting is not secured, some back door stuff could be used and attack your machine.
TL;DR: VPN is useful for privacy because it hides your IP. Just because you delete logs, doesn't mean people can't find you or track your whereabouts.