Among the first acts that President Bush took when he assumed office was to revoke Clinton's signature on the International Criminal Court treaty. It had never been ratified by the U.S. Senate and never will be with a Republican majority.
However, the international "community," (read the Euro Left) may still attempt to arrest and try Americans even though we are not party to the ICC treaty. This is why the administration tried to get a UN resolution.
U.S. Ends Bid for Protection From War Crimes Tribunal (Update1)
http://quote.bloomberg.com/apps/news?pid=10000103&sid=aS68f1LTXTBc&refer=us
The Bloomberg article reminded the reader, The U.S. will continue to seek bilateral agreements that grant protection from the court, according to Cunningham. The U.S. has negotiated accords with 90 nations that have agreed not to refer accusations against U.S. citizens to the court.
The problem is, as you recognize, that the ICC does not limit its jurisdiction to ICC members. The real question is: will Bush take a hard line response if an American is arrested and tried by the ICC? Since he didn't push too hard for the exemption, I don't think Bush will take much of a stand.