I am afraid that using waterproof socks in the same wet shoes still won’t keep your feet that much warmer. Inserting them into wet, cold shoes is still wearing wet cold shoes on your feet.
The evaporation/conduction rates for wet shoes remains the same, perhaps slightly less due to the extra insulation of the Gortex. The dry, warmer socks and more insulation in your shoes is what is keeping your feet warmer. Yes, it works, but it isn’t as effective as carrying a 4oz set of foam shoes. Several MYOG articles on this on the BPL forum. Blue foam is waterproof if not real durable.