no, it is not. The Swan and Dolphin are not 100% owned by Disney, so this is one perk that guests will not get - however, with the rates they have now at this hotel, just get a towncar!
Yep...a towncar is about 85 roundtrip (not incl tip) and you will get a 1/2 hour grocery stop, and go directly to your resort. It is a really nice way to start your trip.