For those of you unfamiliar with An Occurrence at Owl Creek Bridge (spoiler ahead) - this is a terrific story about a Civil War soldier who is sentenced to hang, but escapes his bonds and enjoys a somewhat supernatural escapade, before it is revealed that the whole event was, in fact, all in his head and took place as the noose was tightening. A downbeat and interesting twist ending.
That said, I agree that Brazil does seem to be an homage to this form of story ending, and a little further digging turned up this excellent page on cineleet.com, which delves into the same question.
Essentially, the essay cites several other films that utilize the same ending, including: Carnival of Souls; Jacob's Ladder; Donnie Darko and Brazil. I would also include The Descent (depending in which continent you saw it).
I don't believe there is anything specifically in the scene to link Brazil to the book, other than the plot device itself.