When you use a helpdesk to manage all of your customer conversations, all support requests from the email addresses you integrated will be routed to it. Most helpdesks, on the other hand, use a third-party app to store incoming emails and send responses.
To be on the safe side, some businesses prefer to send and receive email through their own servers by creating a custom mailbox. These servers could be public services (such as Gmail, AOL, and others) or private SMTP and IMAP servers. Most helpdesks also give their customers the option of using their own servers for both incoming and outgoing emails or just outgoing emails.