We played around with this to see if there was an easy way to extract this information, and concluded that the most feasible method was exporting the driving directions using the Save as Web Page menu option, and then parsing the address data from this HTML table.

It is pretty easy to isolate the "address" data from the instructions because they are nicely prefixed by numbers (1 for the Start, 2 for the first stop, etc.) and styles ("waypointnumber_start", "waypointnumber_stop", "waypointnumber_finish").