You can use Smartermail either way. You can have your own domain or you can set up a domain in the software and then import your email from other providers; i.e., google, cox, comcast, etc.... That's how i'm using it right now.
All of my email are retrieved from my cox account and into Smartermail. Once downloaded from my cox provider, it is deleted. The accounts on my Smartermail server goes out and checks external email boxes every 5 to 10 minutes; downloads any new email and remove them from the external servers. All of my devices; i.e., cell phones, tablets, and computers all get their email updates from my Smartermail server.
It may sound complicated, but it's not. I will eventually switch over to my own domain, but for now this is working out well.