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.
True. Until Google decides to code and release their client app, at which point Google will be in direct competition with Dropbox, and any third-party client to Google doc storage would be at a great disadvantage. I would guess that based on the adoption rate, a Google client app is not far into the future.
I think we should look to history to find any clues if Google would release an actual client that would be on par with the dropbox model.
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.