There could be cases when one of your support email addresses would be in cc of a conversation. As a result, the email thread would be converted to a ticket and the conversation would get recorded within your Freshdesk Account.

There isn't any default option to prevent tickets from being created in such cases, as the mailbox keeps forwarding all the emails from your primary inbox to Freshdesk as tickets. But, you can set up a Ticket Creation rule under Admin > Workflows > Automation > Ticket Creation >New Rule, to automatically delete the ticket if the email address in Ticket CC is a support email address.