Not yet. But apparently that's the big 2012 feature Dropbox has been working on.
The point is that they are looking to create 'dropboxes' across the open web, so that you don't have to actually download stuff at your end first. So you could have a folder which you chose to NOT sync with your computer, but instead only used as a web-stuff repo in the cloud, for example. That use case doesn't exist today.