Absolutely! Very few books have also basically changed my philosophical outlook on something as much as this has (I had the seeds of the idea before the book, but the book really cemented specific concepts around computation and thought/consciousness/identity even mean).
Another book that is fairly different, but has had a big impact on some of my views of things, is the Three Body Problem trilogy (specifically the second and third book).
Can you turn it off? The entire universe is 100% deterministic and the "stack" of universes in question is based on the same seed data. So if you decide to turn the n+1 simulation off, the same decision will be made in the n-1 universe. The simulation isn't running on some self-replicating automaton like in Permutation City. Of course the universe being 100% deterministic also poses the question if you can "decide" to do anything, since all decisions are already made.
In "I don't know Timmy" there's a sequence that goes:
"Well, we can't exactly turn it off."
"Why not?" asked Tim, halfway to the door, then stopped mid-stride and stood still, realising.
"Oh."
But you can turn it off without consequence and Permutation City explores the disturbing implications of why thoroughly (with a deus ex machina ending to save causal physics, as expected of an Egan story, physics is what has plot armor).