You have to have a phone line connected to your home to get Centurylink internet service but you don't have to purchase phone service to get the Centurylink internet.
I only have a cell phone and don't need home phone service so I just have Centurylink DSL internet by itself which is cheaper to have since I would never really be using the home phone service anyway.
So yes you can purchase and sign up for Centurylink Internet service without having home phone service and it will be cheaper if you do.