Let's look at it differently. If you're flying straight and level at critical AOA, what would the effect of entering a side slip be? To stall or not to stall?
Another one. Let's say you're just passed the critical AOA in a straight and level flight and are in a stall. Will entering a side slip recover you?
In both cases I wouldn't bet on the side slip being a help. Maybe that's my inexperience as a fresh PPL holder, but I find it hard to believe that in the same circumstances a side slip will reduce the AOA. If only for the roll input required to compensate for the yaw induced roll. Roll input at critical AOA will make the wing with down aeleron stall. That's why you only use rudder during recovery. People die from mistakes such as this, especially on final.