No. If the internet connection is not working your Voicelinx handsets will not be able to receive and make calls.
However, you will be able to log in to the client area and specify a “Follow Me” or “Call Divert” number that your extension can forward calls to if the call is not answered or your phone is disconnected. That number could be a mobile phone or another land-line.
You can change these settings in the “Manage Call Routing” area.