RoundCube can't do this as it's just a webmail interface. What you're looking for is some software to actually synchronize the mail folders. You can either search google for how this is done, or you might be able to find a bash script to run every so often (like every few hours or every day) which just connects via a typical IMAP connection and grabs the info and puts it on your server.
The only other option as to how gMail and other services do this is to log in to the other email accounts at the same time you log in to your main account. Then the messages are read directly from the other IMAP accounts and displayed inline with the rest. So it may not be that they're actually moving files or messages around, but more like they're just aggregating everything for you.