1) Any spam received on your email will pass through as it is to the destination address. The server at the receiving end will consider your cPanel hosting server to be the source of that spam delivering it to their server.
2) If you receive a lot of emails, all those emails will be forwarded to the 3rd party server. And that server will consider all those emails are being generated by your hosting server and consider it bulk mailing and may temporary reject it with errors like this: Our system has detected an unusual rate of unsolicited mail originating from your IP address. To protect our users from spam, mail sent from your IP address has been temporarily rate limited.
3) If you receive a lot of spam, your hosting account and server may be black listed for sending spam.
To solve this problem, we recommend that proper email accounts should be created and email should be fetched using POP3 or IMAP. Gmail for example provides this feature where you can fetch your emails into Gmail. Here is how to do it: https://support.google.com/mail/answer/21289?hl=en (Choose the type of account you’re importing from: A different email provider)