No, the stunnel works only on a transport level and doesn't try to analyze packets. But this may be a good addition to it and shouldn't be that difficult. You may propose the change or pay to it's author to implement.
As a workaround you can start a small webserver like busybox httpd (already in Ubuntu) or Lighttpd or even just netcat and make a redirect with them. But this would be an additional software to start and configure.The current most popular solution is to use Nginx upfront as a reverse proxy. This is more complicated but gives more options.