Powertoad:

A lot depends upon the receiving server and how it is configured. The biggest problem you will have is that of mail relay. Mail servers, (well... good ones....), allow the admin to delineate the addresses it will accept SMTP connections from to prevent spammers from hijacking the server for their "business". For example I have a mailserver where the address block 192.168.0.0/16 are considered "local". The server will accept an smtp connection from any address in that block and forward the mail on to the appropriate recipient's mailserver. If you try to send a mail from your IP, say 222.111.127.145 to an address that is not in my domain you will receive a message saying that relay through this server is not allowed and your connection will be terminated.

Additionally, there are public servers across the internet that do not list the IP address of the sending station in the headers. I've seen this in mail headers but I can't remember where to find these servers 'cos it wasn't of any great import to me.

You could also use anonymizer to send and receive mail.