It would have to be mixed in my estimation to allow the OS Administrator role member to start SQL server and add a SQL user, right. If ONLY SQL logins were allowed, then the Administrator-role-non-SQL-User, could not gain access. One would need to do more severe changes to the SQL Engine dynamics, to allow mixed mode: Thinking 'maybe' [haven't explored it yet] changing the registry entry might allow mixed mode....need to look agian.
WAIT: Google find:
can change the Login Mode via registry