Does GR anywhere says or imply that it not possible to know the absolute motion of the earth? Meaning it is not possible to know the angular velocity of earth without using other celestial bodies as a reference? Does it?
Yes. GR says that there is no such thing as "absolute motion." That's implied by the Equivalence Principle. In the case where you are accelerating (relative to some other frame), GR says that you cannot "absolutely" say that you are accelerating, because any experiments you do to confirm your acceleration can also be interpreted as resulting from the presence of a gravitational field.