Remote preview can do that - but it depends on WebRTC, so just Firefox at first (it's coming to other browsers). It's not actually that easy to add in the desktop build, since we don't run a HTTP server any more, but we could look in to it.
It's an interesting question. Since C3 works offline as well, how do users preview their work in different browsers if they don't have access to the Scirra servers generating the link? Also, if those servers are down by accident or maintenance, how do the users preview in other browsers?