Yes, BoldDesk allows you to add an email response as a private note using specific email actions. To do this, include the following syntax in the body of your email:
#private
When this tag is used, the content of the email will be added to the ticket as a private note, visible only to agents and not to the customer.
For more details and other supported email actions, refer to the official guide: Email Actions – Update Ticket Properties via Email.