You really think us young adults who have grown up in a world never knowing a time without internet would be able to actually pull that off? I know I couldn't, even if I tried.
As soon as your calls makes it to a cell tower it gets encapsulated and routed over a telco's network. Any call you make from one call provider to another will traverse the internet. And depending on the extent of the thought experiment for disabling the internet, you could include disabling individual telco's networks as well, meaning you won't be calling anyone... except for maybe someone on the same tower as you.