If you are talking about https://moodle.org/plugins/view/auth_googleoauth2
the answer is yes, a user can have a googleauth account on your moodle as well as a manually created account or an account auth vs LDAP ... however ...
the accounts are NOT the same user to Moodle.
The above auth addon creates user names using 'social_user_#' as the login where # is a sequentially assigned number 1- whatever.
The manual/LDAP accounts will use whatever is given to user ... example: LDAP might use first iniitial of first name and lastname as 'login'. So my account would be ktask.
ktask is NOT equal to social_user_# thus anything I do as ktask (submitting assignments, taking a quiz, etc.) is for ktask ONLY and not for any other users on the system.
In anticipation of your next question ... can they be merged ... probably ... one time ... but one account auth will have to be chosen over the other and syncing will not work both ways. In other words, no.
'spirit of sharing', Ken