The only way you could do that is if you never signed off... If you timeout to the server it will still say you logged off anyway. It's OSCAR and MSN and all the others that broadcast that message... Nothing GAIM or any other client can do about it.
They are more than likely looking to do this so that their support through AIM appears to be online all the time. An alternative that allows you to have several different AIM connections at once going is Trillian. Another option if you are looking to use this for support that you might really want to look at is ChatStat.com