Local and Domain logons are distinct keep that in mind. I would create the username and then try it out myself. Usually its the group the user is in that defines his/her rights to log on.
Good Luck.
They are distinct
except on DCs (Domain Controllers).
The rest of the advice is good - it's much easier to manage domain security using groups than individual users, but be aware, in most cases (not this one) when you've added a user to a group they will need to log out then in again before the system recognises their new rights.
Only add a user to the 'Backup Operators' group if you really don't care about security. It's a bit like making them God in most setups.