If the phone switches networks, then it would have to create a new connection. The router can behave the way you describe by having a server listen on port 80 (HTTP) and then proxying data to a new session on HTTPS. 

There is the [SSLStrip][1] attack that is similar to your description but it involves many more steps.


  [1]: http://www.thoughtcrime.org/software/sslstrip/