Your setup should work... you will always have to write "sudo" followed by users password before the "userdel" command

During the Ubuntu desktop installation the installer asks you for an username and pass, since desktop installations have mostly one active user this user will become also the system admin (server installation or some other distribution may ask for the root password). This user will be added to the admin group:

# grep "^admin" /etc/group

admin:x:115:pavol

and in the sudoers file is an entry that any user in admin group can run any command on any host as any user:

# grep "admin" /etc/sudoers

# Members of the admin group may gain root privileges

%admin ALL=(ALL) ALL

So if you are in this group you don't have to add a new entry for your user and userdel command.

However if you create a new user, he/she won't be by default in the admin group and won't be able to run the userdel command without a proper entry in the sudoers file

# adduser tester

# adduser to_be_deleted

# su - tester



$ /usr/sbin/userdel to_be_deleted

userdel: cannot lock /etc/passwd; try again later.



$ sudo /usr/sbin/userdel to_be_deleted

tester is not in the sudoers file.  This incident will be reported.