afaict this is android only. took me about 10 minutes to figure it out, they were super sneaky with the wording of their press release. thanks for wasting my time :(
"now with Dropbox you can automatically upload from just about any camera, tablet, SD card or smartphone — pretty much anything that takes photos or videos!"
So it was confusing.
I looked through the iPhone app and there isn't anything about it. However I updated the desktop client and it recognizes plugged cameras or phones and ask if you want to import the pictures from it.
Before complaining, you must ask the quintessential iOS development question: "is there an allowed API to accomplish it?"
The Android corollary is: "Does it work on my ARMv6 Android 2.1 toaster? And can it use the hardware acceleration features provided by Qualcomm processors?"
As far as I know, the answer to your first question is "yes". (I haven't tested it myself but I have seen it used in apps to display a custom photo picker. E.g. in Camera+)
"An instance of ALAssetsLibrary provides access to the videos and photos that are under the control of the Photos application.
The library includes those that are in the Saved Photos album, those coming from iTunes, and those that were directly imported into the device. You use it to retrieve the list of all asset groups and to save images and videos into the Saved Photos album."
I'm not very familiar with the background process APIs, but from my understanding of it, I'd be surprised if you were able to do that. In my comment I was mostly thinking of automatic upload as the user uses the app itself: opens Dropbox to check out a document and it automatically gets the new pictures without the user having to remember to do it.
I recently purchased an android phone (Samsung Galaxy Nexus) and I noticed this happening as early as this Tuesday (the 24th). I was wondering why that was happening... cool!
