It is possible.
I'm just finishing second version of such a socks. The first one was made of GTX Paclite, it was ligt and lasted for a while, but is not really waterproof any more. The new ones are made of 3 layer goretex, so I hope they will be more durable and worth the double weight. Sealing the seams with tape is not easy, but doable.
PM me for a pattern.