If there is a simple google api, some third party / open source developer, not having to worry about the backend infrastructure required, might create a client app to do this, which would compete with dropbox to some degree.
They are notoriously reticent to do anything that installs on a client machine, Chrome being an obvious exception. I'm still skeptical they would release a client but it's definitely within the realm of possibility.
It may be more likely that either dropbox or other 3rd party tools will get into the game and start integrating their offerings with this.