Not any more than itās fair to assume that, by showing the Barge of the Dead, or the Miranda-class, or the Oberth-class, or the Galaxy-class, or the proto-Klingons, that VOY: āBarge of the Deadā, ST II, ST III, TNG or TNG: āGenesisā took place in a reality with different class ships or people.
The Mirror Universe question is a separate one, to which there really is no good answer because weāve only seen crossovers from the Prime Universe to its Mirror Universe counterpart. A bigger question is whether or not the Mirror Universe we saw in PRO: āBroken Mirrorā is the same Mirror Universe we see in DS9 because there the Terran Empire seems to exist again.
But that still doesnāt mean DIS is in an alternate reality.