Yes, pointing the highest priority MX record to "Server #1" and the lowest priority MX record to "Server #2" should work for your client's requirement of using two email servers.
When someone sends an email to [email protected], the sender's email server will first check the MX records for your client's domain to determine where to deliver the email. If the highest priority MX record points to "Server #1," the email will be delivered to that server.
If "Server #1" is down or unavailable, the sender's email server will try to deliver the email to the next highest priority MX record. If the lowest priority MX record points to "Server #2," the email will be delivered to that server only if all other servers with higher priority are down or unavailable.