Sentience is an illusion insofar as it is can essentially be defined as an emergent property of specific instantiations of general mathematical forms. So it can be modelled mathematically, but when an instantiation reaches an arbitrary order of complexity it is deemed "sentient"; it is really a smooth gradient and the cutoff point for when something is "sentient" is completely arbitrary. Humans being humans, we like to place the cutoff point just below our own capabilities but this isn't meaningful in a definitional sense.
Many of our "illusions" are known to be illusions precisely because they can be mathematically modelled. Our brains do not have the resources to see through the illusions no matter how hard we try (per the mathematics as applied to general computing hardware), but we can be aware of the fact that what we are perceiving is illusion. The nice thing about mathematics is that we can model our inadequacies in addition to being able to model our competencies at the same time. We can actually place the human brain along the computing engine gradient between zero and infinity (intelligence systems being more a measure of memory than processing capacity) by modelling the general limits of human capabilities.
As I stated previously, "free will" is essentially an illusion that is a specific mathematical consequence of having insufficient mental capacity (a memory limitation in this case). You can even see this behavior in software (optimal universal predictors modeling a finite state process as "random" because they have insufficient encoding memory to see it as anything else even though a human can see that it is finite state). We see simple systems as being finite state machinery with predictable and deterministic results that have nothing to do with "free will"; these systems fall within the model capacity of the human mind. Other processes look like "free will" which an objective observer with more memory (like a computer) may analyze to be otherwise. One could say that we can mathematically model the point where "finite state machinery" starts to look like "free will" to another finite state machine.
Sentience is a little different, in that it isn't an illusion per se, but an arbitrary designation of complexity. It could be argued to be a meaningless term, as all constructs that meet certain mathematical criteria could claim to define "sentience". A computer that was properly programmed to be vastly smarter than humans could very well determine that it was the base level that defines "sentience", and that humans were just animals that are more clever than most.