This is from the AOL FAQ:

Q: Why am I unable to connect to AIM through my company LAN? In the past, I made the connection with no problem.
A: Ask your system administrator to update login.oscar.aol.com on the LAN's DNS table. Also, ask the administrator to make sure that Port 5190 is open for outbound TCP connections. (Other ports can also be used. If your administrator decides on a different port, then you can specify it in Connection preferences.)


As you can see there is a clearly defined port which it seeks to make connection. Unless AOL is monitoring every port on its server for AOL connections, I can't see how random ports are used.