I just created a dropbox account to test this out. Obviously there are no existing files in it. I looked for a button to create a new file and could not find one.

If dropbox does not have a create file call for you to use, perhaps you could have the app create an empty filename and upload it automatically and then edit it as an existing file?

Edit: Never mind, I finally noticed the buttons on the bottom left. That was quite unintuitive for me--I never look at the bottom left for application buttons. Is this something that textmate does?