OnDemand does not have the ability for System Admins to turn off the auto generated system e-mails while performing administrative tasks such as imports. Currently, a ticket must be created to have Atlassian support team disable it for you. This means waiting for it to be turned off, then waiting again when it's time to turn it back on.

Ideally, it would have the option to control what groups receive these emails since some are helpful for the system admin for troubleshooting. However, even the ability to turn off completely while performing system tasks would be helpful.