This is called IP Spoofing
Quote from wikipedia:
In computer networking, IP address spoofing or IP spoofing is the creation of Internet Protocol (IP) packets with a forged source IP address, with the purpose of concealing the identity of the sender or impersonating another computing system
Of course, you could replay packet do initiate a DDOS on mail server, but reply packet will never reach source, so full TCP connection will not work (unless attacker are located in one router in the middle between you and real location of spoofed ip.).
But in other way, spoofing IP in mail header could be done too, see this second quote from same origin:
The term spoofing is also sometimes used to refer to header forgery, the insertion of false or misleading information in e-mail or netnews headers. Falsified headers are used to mislead the recipient, or network applications, as to the origin of a message. This is a common technique of spammers and sporgers, who wish to conceal the origin of their messages to avoid being tracked down.
So IP Spoofing for mail forgery is at some different level, but could be too.