This is exactly what I am using iAlert for currently. I have iAlert
running constantly on my Lion server machine, with a symlink of
~Movies/iAlert pointing to a Dropbox folder. I use Hazel to delete
anything older than 48hrs (free Dropbox verison), and to rename the
file based on the creation time: YYYY-MM-DD HHMMSS.mp4. It's not
pretty, but it works.
I agree with Shad, firmware Dropbox would be something to write home
about.