Dreamwavering,
You probably need to be more specific on what you are trying to achieve with Postfix. If you are trying to sent email out (e.g. fax to email or voicemail to email), there is no need for a registered domain name on your Elastix box.
For those that already have a domain name, e.g. mydomain.com, it is common practice to setup the domain on your ELastix box as mydomain.local.
You setup the postfix config to use mail relay, which is normally via your ISP. This will allow your system to send out email.
If you are trying to receive mail in on the ELastix box, then no
email@ipaddress.com will not work. You need to register a domain, and point the MX records to your ELastix box.
Have a read of Elastix WIthout Tears, which has a reasonable section on Mail setup, and also have a read of Elastix & Network Setup, which talks about the .local domain name.
If I have it all wrong, as I mentioned, you need to be more specific on what you are trying to achieve.
Regards
Bob