Quan Chi's intro to Sub Zero is 'I have your brother's soul'

We know the Kamidogu dagger Kano slices Sub Zero (likely Kuai Liang, considering we see Bi Han kicking cyborg ass in his standard costume) causes his eyes to glow red, like all the Kamidogus seem to do.

Do we think this is maybe how Quan obtained the soul of that Sub Zero?