Yes, you can set up an automation rule to achieve this. For example, if you do not want the new ticket created notification to go out to customers reaching out to your support through 'Chat':
- Go to Admin > Workflows >Automations
- Click on the New Rule button.
- Name the rule
- Under "On tickets with these properties" select "In Tickets," "If source is Chat"
- Under "Perform these actions" select "Skip new ticket email notifications"