[Coda]

No, it doesn't, because it's not a cyclic repetition. Every selection is independent of all of those that came before it.

Okay, that's not strictly true. There actually does come a time where the sequence will absolutely exhaust the accumulated entropy, since it's not likely that the game bothers with refreshing the entropy pool after booting up. But that would take a minimum of... uh... *tries to crunch numbers* ... um... okay, that would take so long that there's not even a way to name that number meaningfully. If you could somehow keep a computer running the whole time, it would have gotten about two parts in a googol of the way through the cycle by the heat death of the universe.

EDIT: Okay, so theoretically speaking if you let Monika yammer on for a whole day and do some clever math you can learn enough about the underlying chaotic system to start making predictions about what she'll say next with accuracy better than random chance. Frankly that's probably more effort than it would take to start predicting a human with that kind of accuracy.

EDIT 2: That's assuming that once she starts into her spiel that no other random events are taking place. If, for example, the animation in the background draws on the same source of random numbers, then that DOES reintroduce chaos into the system, and it conceals data that would be necessary to perform the above analysis, which pushes things right back into nondeterminism.