Yes!

You can receive updates via the web interface, or via callbacks when an SMS is sent, and when it is delivered to the end-users handset.

Web Interface

When it has been sent, you will see the message status as "Sent" in SMS manager.

Once it has been received on the remote handset, the status will update to "Received".

API Callbacks

Please see the API documentation for full details.  The status code for sent is 2 and the status code for received is 4.