Travis Bailey: The page would have been cached by a search engine, which most engines could likely perform a diff from the last crawl. It would be pretty easy to see that the only thing that changed is one tag in the src code. So probably not.
Cathy Gray: There is a patent called the caffeine update (i believe that’s the name) that covers this. But it’s not relevant for everything aka not a high priority one.
Ammon Johns: Cathy Gray the Caffeine update was a core update in the noughties (2009) that added the ability for Google to use more data on dates and freshness in new ways. It`s a core update, so has been a part of Google ever since.
Buth Main: The short answer is no. You can fresh your content, make it relevant. Do keywords analysis to fresh your content, analyse trends.
Ammon Johns: It can make the page rank lower in any query that favours established, knowledge based answers too. Stuff where the newest version isn`t especially more valuable than the tried and tested.
Richard Hearne: You may be conflating a tactic used to abuse News results? Some publishers update the publish date without updating the actual content to make News content appear more fresh for Google News surfaces. Unlikely to have any impact in Organic results IMO.
Can constantly updating the publish date or in the sitemap to make the page appear fresh increase search rank? 
