The technology does exist for modern aircraft to fly the route unaided. Pre 9/11 I jumpseated a 777 from Brisbane to Kuala Lumpur, and was assured by the Captain that without his input the aircraft was configured to track across South East Asia to Kuala Lumpur, descend, approach, land and taxi off the runway before further input was required.
One small step...
On another plane, sorry about that, railways are increasingly going over to driverless operation, apart from the aforementioned DLR, the Kuala Lumpur LRT system 2 is entirely automatic, based on the Vancouver Skytrain. And work is currently underway to impart the same technology to Londons Underground.
In your lifetime, most definitely yes.....
The transfer of control is similar for aircraft and trains, the one will require a co-ordinated regional ATC, the other will require Centralised Traffic Control (CTC). Both systems are already well established worldwide.
Takes off anorak and pops over to the pub...