Is an MX-record required on a domain to send mails only?

Consider the following scenario:

  • I have a online-shop that sends mails with noreply@shop.mydomain.com
  • There are no MX-records for shop.mydomain.com as no mail to this domain is wanted
  • There is a valid SPF-record for shop.mydomain.com

To be sure that mailservers will accept from noreply@shop.mydomain.com, is a MX-record requried for shop.mydomain.com or not? (In concerns of anti-SPAM systems)