Yes, both things are possible. On the e-smith, you need to set the delegate mail server option in "E-mail retrieval" to the ip of your exchange server. You'll also need to set the exchange server to hand off mail to the e-smith.
However, you seem to be confused regarding public ip's when using a DMZ - if you put the exchange server on the DMZ, by definition it wouldn't have a public ip - only the firewall would be publicly visible. You don't need to change the MX record if the firewall is on the ip that the MX is pointing to, all you'd need to do is to open the pin-hole in the DMZ to point to your designated mail machine.