Could the klingon Empire have a population of a trillion? Don't see why not, we see mostly biological/ethic Klingon on the show, but there has long been an unofficial belief that the Empire has other species as part of it. Everything from second class citizens through out and out slaves.
A total population of a trillion? Sure.
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Although there is no hard canonical evidence confirming or refuting the idea of a Klingon Empire with a trillion people, I find that hard to believe. We have seen absolutely no evidence of Klingon slave species, and it is unlikely that, even if said species existed, they have had much reason to propagate hafter being subjugated.