A google search for 'Kwatz' generates quite a number of references within Zen and has a history with it. From what I see, it appear that the term is an exclamatory utterance (a nonsense word ?) that does not allow any analytical or intellectual interpretation. Am not familiar with 'Fall of Hyperion' but you state that the term is interjected in koans and that would be very consistent with the Zen use of Kwatz and makes sense given the context you state.
From Zen:The Solitary Bird
Kwatz! is a Zen stick. When the master does not have the stick with him, this is a substitute for it. He shouts, "Kwatz!". With that shout he his hitting you to understand a simple thing. No question, no answer. Just be.
Kwatz! It is a sound, found by Zen, that shatters your mind. At least for the moment, you simply remain silent, amazed - because it is not language, you have not expected it. ...
From Awakening Way Zen - Kwatz.
"Kwatz" is a term fondly regarded by many Zen students because it humorously and engagingly sums up 9th Century Chinese Zen Master Linji's frustration with the idea that "truth" or "meaning" could be something words could ever hope to represent.
There are records of it's (Kwatz!) use within Zen a millennia ago . I came across a very dry article in the Sociological Quarterly with this tidbit.
The Chinese Zen master Linchi (Rinzai) (d. 866 C.E.) was famous for responding to questions by exclaiming "Kwatz!" which has no literal meaning.
As additional support for this interpretation, your question says the name of the AI is Ummon. This is also the name of a Zen master (Ummon Bun'en Zenji [Japanese]) who lived during the golden age of Zen in T'ang Dynasty China (864-949 AD). He was known as Un Num in Korea and Yun Men in China. See Ummon