No. An MX record points to your inbound mail server and it is quite common for the outbound mail server to be different than the inbound server. We have never heard of anyone having an issue with their email getting blocked because their inbound (MX) server does not match the outbound server.
It is a common misconception that deliverability issues can occur if you point your MX record to a server separate from your outbound mail server. This myth stems from the fact that many email servers do what is called a “reverse lookup”. However, this reverse lookup is against the IP address of your outbound server and has nothing to do with your inbound (MX) mail server. The purpose of this lookup is to confirm that the IP that you sent your message from points to a hostname that points back to this same IP. That confirms to them that you are not spoofing the hostname of your outbound server.