Yes you certainly can! Voila doesn't require an internet connection to give you the great benefit of wireless sharing your content to the 2Share Essentials screen. Of course it does require a network connection.
*2Share needs to be part of a LAN (Local Area Network) and have an IP address (static or dynamic) in order to work.
Please be aware that when you use Voila without internet connection, you cannot make use of the Voila via the Google Chrome browser!