domain name system - Does adding new MX record go along with adding a new CNAME record?

If I add an MX record for a subdomain email address, do I also need to add a CNAME for that subdomain?

For example I want email addresses like *@mysubdomain.mydomain.com to be handled by a different server than *@mydomain.com so I add the following record:

MX mysubdomain handled by mail.anothermailserver.com with priority 10

Do I also have to add a CNAME as follows?

CNAME hr is an alias of 12.34.567.890

While I have the following A records:

A * points to 12.34.567.890
A mydomain.com points to 12.34.567.890
A mail points to 12.34.567.890