The short answer is no - a domain can still send or receive emails even if the MX (Mail Exchange) record does not show up on a DNS search.  

The long answer is that it’s a little more complicated.

It always best to have an explicit MX record for a domain because it enables explicit routing and management. You can also implement load balancing by assigning different priorities for multiple servers. Overall, it is more reliable to have explicit MX records.

However, if there are no MX records, the sending server will attempt to deliver email to the IP address returned by the A or AAAArecord.  This will happen both ways - when the domain is sending email or when another email server attempts to send to the domain. If the A record route fails, the email server will bounce the email. In many cases, it is possible to follow the trail to identify MX records associated with the A record.

There is a third scenario which is less common but may occur with organizations who have implemented solutions for Distributed Denial of Service (DDoS) attacks and Bot management. This may be true for large organizations or those with a high profile. To insure against these attacks,these organisations may use solutions from cloud providers such as Akamai or Cloudflare. They provide solutions that effectively mask the MX records for the client organization to ensure they are not easily discoverable by performing DNS lookups. The MX records exist and can be seen by mail servers but not by other users. Alternatively, emails may in effect be sent to the cloud provider and forwarded onto the client. If the PTR record for the A record point to a cloud provider this may indicate this type of solution.

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