Yes and no. Since cowl would be alt Harry under that idea, I don't think he'd have bob from this reality, even evil Bob. But I could be wrong.
*Harry, cowl and Kemmler... And the walkers, all have this weird symmetry to each other... Like Fearbringers sack clothes were based on Harry's duster after I lost all it's color... But it's also the same sort of functional effect as Kemmlers robes(from... Warhammer I think it was?) That are enchanted. The connections are masterfully done imo