Just got back from an 18 day trip to Scotland, and my husband travelled with his extension letter. Everything went fine with that! This guy in Edinburgh airport didn't know what to do with it (it was the day after the car crash in Glasgow so security was tight), but another lady came over and showed him what to do. He had the nerve to say to us "you know you really should get yoru greencard updated, this letter makes things awkward". We mentioned something about the US taking 9 months or more to update greencards. I hate ignorance like that. We just let it go though, because we know we've applied and we know the letter gives us the right to travel!
It was smooth sailing when we got to US immigration of course (and he was able to go in my line! - Newark).