No, that file is located in the nix store and linked back, If you become root and try to edit /etc/hosts It will complain that you cannot edit the linked file.
If you go and try to edit the store directly you will meet the same kind of dead ends because /nix/store is a ro bind mount
With enough root access, time and persistence you could eventually unwrap its flavor of immutability which is why I said mostly immutable. Compared to most operating systems where you can just slip a quick edit into a cron job it's leagues ahead.