This feature would be even more useful if you could drag and drop pages that are already loaded in a different tab. I've tried to do that in Firefox, Opera and Chrome, but it only worked well in Chrome. The other browsers added some new characters to the URL and Google had to translate error pages. Chrome is already integrated with Google Translate, so you don't have to use this feature.
You could also select some text from a page and drag it to the input box (ignore the yellow box this time). If instant translation is enabled, you don't even need to click "Translate".