I still think this is an interesting question and to help the discussion develop in place on any other meaningful input coming forth I will add the following.
Assuming the viscous liquor contains air within the body of the product (the OP has stipulated air/liquid mixtures,not free air entrained at the inlet) - as it enters the impeller eye it may or may not expand depending on NPSHr/NPSHa, if there is an NPSHa margin over the NPSHr (there must be some difference in pressure at the impeller eye otherwise flow won’t take place) the air will remain within the product and likewise we can assume that the air will remain at approximately the same volume. Once it fully enters the impeller the air will be gradually compressed (pressurised) as it flows thru’ the impeller, this means that the "product" will reduce in apparent volume translating to a reduction of volumetric output performance.
However, if the air remains within the product, the pump will remained primed - which I guess is the main aim anyway and a pump that keeps pumping at whatever the overall hydraulic efficiency is, in my mind 100% efficient compared to a pump that is not pumping.
This may well be a bit of nonsense but it is the middle of the silly session and it might get some interesting comments anyway.