The SQL Server Geodatabase Privileges help page states that "Alternatively, the upgrade can be run by a user (other than sde) who is in the db_owner database role or sysadmin fixed server role."
My organization has a team of database administrators who typically manage our databases. If they were to upgrade the geodatabase, am I correct in understanding that they would need access to desktop GIS software (ArcMap or ArcGIS Pro) to complete this task?