My external customer's are not receiving ticket event notifications, like when a comment is added to a ticket. But, they are able to receive mention notifications, like when a message is sent using the @ symbol. These accounts can be gmail, yahoo, or the customer's custom domain. Atlasian support says both notifications are sent out the same way by atlasian.
I would assume if one notification worked, they would both work. I don't know why google would block one type but not the other.