In theory, yes. But I've just tested it out and it appears that dropbox don't allow remote embedding....I'll test again later, but it looks like a 'no' right now.
Update: I've determined how a dropbox url can be modified to allow hotlinking. There's no change needed to plugin to actually support this but below is what you would need to do now to have it work.
Further update: I've just spent a couple of minutes putting in a little function to do the manipulation needed, so that will be in the next update I release (v1.0.6)
Example url provided by Dropbox when creating a share link is: https://www.dropbox.com/s/aewhi52igjvxp18/video1.mp4?dl=0
Remove ?dl=0 from the url
Change www to dl
Submit post
Without the url manipulation:
With the url manipulation:
At some point in the future, maybe. I don't own, or plan to own, a license for Downloads so for the moment it's a 'no'