Send Email through Cayenne serial connection
No, the Arduino cannot send emails directly through serial. The communication channel you have set up is a direct connection between the Arduino and Cayenne. It cannot be used for anything else other than communicating with Cayenne.

However that doesn't mean you can't try and see if there is some way of making Cayenne send emails for you. Having never used Cayenne I cannot comment on this aspect. You would be better off consulting directly with Cayenne and their users through their forums.