No, Viasat Internet does not require a Phone Line. Viasat satellite internet functions without needing any landlines, including phone lines. 
Viasat internet services, including Viasat Voice, use satellite beams between the satellite dish installed at your location and the designated satellite for all communication.  This means nothing but sky between you and the internet.
It is the need for landlines that prevent many remote areas of the United States from receiving traditional internet services.  Telephone lines and cables can only reach so far.  This is a shortcoming not experienced by Viasat satellite internet. With Viasat, any location under American sky can have access to high-speed broadband internet.  Viasat’s latest satellite launch, ViaSat-2, now delivers internet at up to 100 Mbps to many areas in the United States.

What if You Want to Bundle TV and Phone with your Viasat Internet?

Surely these services would require some kind of a phone line, right? Not with Viasat.  When you bundle your phone (Viasat Voice) or your DIRECTV with your Viasat internet service, everything goes through your existing satellite dish installation.  No phone lines required.
The Viasat Voice system allows you to integrate your phone service into your existing Viasat satellite internet set up.  You might be worried that this could use up your monthly data allowance.  Fortunately, all phone calls via Viasat Voice use a separate data channel from your Viasat internet, allowing you unlimited calls without using up any of your internet data.  Viasat Voice having its own prioritized data channel also means that heavy network traffic won’t affect the quality of your phone calls, even if you put your Viasat internet into vacation mode.  With Viasat Voice you get unlimited local and long-distance calls to anywhere in the 50 United States and Canada.
At the beginning of satellite internet technology, phone lines were often a necessity.  With Viasat’s modern implementations of satellite technology, all downloading and uploading require just a satellite dish and a modem.  This is great news for rural internet users who don’t have access to land-based internet lines.  With no phone lines (or cable or fiber) required, Viasat truly can reach the remotest of locations.