Yes, but no...
For a basic user, who does not expect to be doing anything special beyond opening existing programs, or using programs downloaded from the package-manager its possible to never touch terminal.
I have two kids who daily drive Manjaro based light gaming PC's, they never touch the terminal, but they also dont administer their systems, I do.
I do use the terminal, frequently for updates, and some specialized tasks like minecraft mods which require unpacking files and sometimes fixing permissions.
So my TLDR, is that its possible to be a USER without touching the terminal, but I dont think its possible to be an administrator without.
or, I can SSH from my computer in a different room, and do it with one CMD in terminal :)