Does this module send notifications to clients when bulk order status changes are made?

Yes, if you configure Mass order Actions to send those notifications.

There are two options to do that:

1) In System > Configuration > Mass order Actions you can choose default settings for notifications:

Magento Mass Order Actions - Amasty

 

2) When applying a mass action from Magento order grid, you can set the “Notify Customer” option to No or Yes:

 

Magento Mass Order Actions - Amasty

See more details on Mass Order Actions page
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