Is it legitimate to use dropbox as file storage for my site?

Look in to Rackspace Cloud Files and Amazon S3. You can hotlink directly to the files.

Alteratively, have your users use an image hosting service like Flickr or photobucket, and have them provide links instead.

Dropbox has bandwidth limits. I use it quite often for running simple static websites for internal testing, but it there are limitations.

Take a look at this: https://www.dropbox.com/help/45