Update: During an interview on YouTube Live at E3, Bethesda Game Studios’ Todd Howard offered some clarification on how Fallout 76’s features will work.
Howard reiterated that you cannot play offline, and clarified that while you can play by yourself, you will still see other people in the world. There will be no NPCs (outside of robots), and Bethesda intends for players to fill the roles that they normally occupy, from vendors to the raiders you encounter on the road.
PvP settings are still being dialed in, Howard said, and will likely offer some flexibility for how you want to play. “We want a little drama there without them ruining your game. We don’t want to be griefy in any way.”
Source: IGN.com Fallout 76: You'll See Other Players While Playing Alone