Depends on the method used. Virgin Media in the UK intercept HTTP requests (and send resets to HTTPS connections), so even tunneling my DNS traffic over a VPN doesn't help.
Also I am not even sure it is possible to intercept any traffic over VPN without having the keys, so not sure why tunneling over VPN is a problem , DPI and MITM techniques are not even used by the Chinese government for the most part and people can generally VPN out if they want to.
Over HTTP, you get redirected to http://assets.virginmedia.com/site-blocked.html Over HTTPS, you get ERR_CONNECTION_RESET (Chrome)