Hi Graeme,
Most hosts will allow you to set the "Send From Email" to anything you want. Some restrictive hosts, however, require it to be an email address on your domain. Some even more restrictive hosts require the address to exist in your control panel as an email account or forwarder.
Try it with a test list. If you receive the message at a remote address (one not on the same server/domain) all should be ok.
Regards