MS may be prepared to deliver something like that, since they have the old Danger/Kin stuff which was based on what you would call a fat cache architecture. MS also appears to be moving to a single-runtime (WinRT) future, so the "same" app may be available on phones, tablets, and desktops.

The idea of migrating an app session between devices is going to be pretty difficult in most cases because people use different apps on different devices to access the same data; Twitter is an extreme example but there are plenty of others.