Electric Amish, I do not know the answer to your question 100%, but I can relate to you that I set up ICS to work with two systems and was able to connect to the same server on both machines playing Quake3.
Here is my 'educated' guess.
Yes, the same public IP address (assigned to your sharing computer or server) will be communicated to the game server each time you connect with a machine in your network. The key thing here I believe is the name of your character. Logically, if you have a different game player name for each computer for which you plan on connecting to a particular game server, and if the server allows multiple accesses from the same IP, it should work. If the name is the same (although I've never tried this in Q3), it seems likely not to work as the game server has no way of knowing that there is in fact more than one computer attempting to play, unless of course the game server is able to do NAT (network address translation), but I doubt that.
As far as ICS is concerned, while not as full-featured as NAT32, it does have a basic firewall and has better security than if you weren't using a firewall at all.