Found this out the hard way at the JFK GE booths yesterday. Despite being completely approved for GE, paying the $$$ (for both the UK and US checks!) and having the gentleman at Bowling Green explain how to use my visa in the GE booths, L1 visas apparently aren't accepted and we must still use the excruciatingly long lane. When you try to put the visa in the GE booth it says unauthorized document.
No refunds for GE.
(I'm a UK citizen by the way).