[hmng]

Not really, SMTP relays will only send messages once, to one server.

But it’s not receiving that is the problem, that is generally fine, if ports are open at ISP / network level. It is the sending that is often tricky. Sending email on the other hand can be done from multiple servers (if SPF correctly configured) And nothing prevents you from sending email directly from your own relay. You could try that, and reception would not be affected.