It would be cool, yes, to act like a first-party Dropbox client and have full access to my account via open tools.
But in the meantime, they do have a python API and SDK:
https://www.dropbox.com/developers/core/sdks/python
This lets me setup a sub-folder under my account with no more than python present on a machine and perform upload / downloads of content. Nothing processor architecture-specific about it. And with python modules like https://pypi.python.org/pypi/watchdog it's pretty trivial to trigger a re-upload of local content when it changes. The API provides counterparts for detecting changes in remote content (the /delta command).
In fact, this is how I've got Dropbox access running on my gen1 AppleTV :)
I'm more generally interested in the process of reversing of the code and protocols.
Do you also have Dropbox installed on a desktop at your place?
Maybe you could co-monitor your desktop Dropbox folder using this: http://sparkleshare.org/
It appears to be a Mono/.NET based project, but apparently there's Mono for ARM.
There's probably other options as well - just a thought :)
I wonder how long that implementation will continue to work. The official Dropbox client auto-updates (well, the Windows one does; Linux doesn't, afaik), so Dropbox can almost change the protocol whenever they like.