Well...
Coast to coast can mean a few different things. I think I saw 3,400 miles in one of the threads a while back, so I'll use that. If you assume 300 Wh/mile, that means 1020 kWh (including the initial ~75 kWh charge, so 945 from the extender.)
Current demonstrated Aluminum-Air batteries run about 1300 Wh per kg. Some folks expect to see 2000 Wh/kg soon, and theoretically it might someday be possible to build one at 8000 Wh/kg:
Aluminium–air battery - Wikipedia, the free encyclopedia
At 1300 Wh/kg, 945 kWh is 727 kg - about 1600 pounds of aluminum air battery. Probably not practical (though I have no idea what fraction of that is the plates - so by using a smaller battery and replacing the plates a couple times you might save some of the weight.)
At 2kWh/kg, 945 kWh is about a thousand pounds (423 kg) - still a big stretch, but technically doable if you don't have much else in the car.
At the theoretical limit of 8 kWh/kg, 945 kWh is 264 pounds (118 kg) - easily doable.
So depending on exactly what Tesla/Alcoa bring to the table, the answer is maybe - but it likely won't be easy for a while yet. Of course, this assumes you're driving it completely nonstop, using keep awake pills and diapers for the couple days. If you stop even a couple times to eat and charge, the requirements go down a good bit.
It is a great solution for people living in places that don't have much charging infrastructure who need to take road trips on rare occasions (Alaska? Northern Canada? Central/South America?) - especially if the plates are easily replaceable and Tesla/Alcoa create a mail order system for exchanging plates.
Walter