It's been a couple of years since I watched it, but I don't recall the GBLA being mentioned in the film.
For anyone interested, the film we're talking about is the 2015 documentary "Bitter Lake" by Adam Curtis which tells the story of how an agreement signed on the Great Bitter Lake back in 1945 could have had an unexpectedly huge impact on how the modern world developed through the next 60+ years.
It's long, but entertaining and as always has a great soundtrack: https://www.youtube.com/watch?v=84P4dzow1Bw