The answer is yes, we can. Here a sneak peak on the script. The example database will be included with next plugins:
The API is explained here and you can sign up for a developer key here.
The script itself is not that difficult. First we start a new CURL transfer and set a lot of options. This includes setting up a form with the various parameters for the service. Than we perform transfer and show debug and result texts in some fields for debugging. Once we closed transfer, we can parse the result json and get the state and the url. If state is not okay, we show dialog with error, else we got our short URL.
PS: This would work similar from Xojo, too.