Yes. You can easily turn off notifications for your business mailbox. Since everyone with access to the mailbox has their own personal settings, each user who wants to disable notifications must do so individually.
In the Kivra app:
Go to More > Settings > Notifications.
On Kivra's website:
On your computer: Click Settings > Notifications and email.
On your phone or tablet: Click Menu > Settings > Notifications and email.
In the settings, you can then deselect the notifications you no longer wish to receive.