No, dropbox is going in the wrong direction. The direction is going to be smaller, faster, portable HDDs. Thumbdrives are already common at 64gb, and SSDs at 256gb. People already carry around a lot of data on their phones and, more to the point, they already carry around a device as large as a phone. Current gen SSDs are about that big. It won't be much to get people to either carry around a second, similarly sized device, or for the technology to just adapt to allow your phone to store terabytes.
Those are already happening; when finally mature, why would you use the cloud? With increasing proliferation of per-byte charges for data, and with the ENORMOUS gulf in access speeds between SATA and the most common internet plans--a gulf that's unlikely to shrink for years, perhaps decades, as both technologies make their own, separate, speed advancements--people aren't going to spend more money for slower access to their own data that they don't even control.