Could hashimoto's encephalopathy cause a circulation/nerve problem like mouth and fingers go numb when standing up/lying down and blood pools in legs?

Not really: "Encephalopathy" (no matter whose name precedes the word) simply refers to a state of altered thinking/understanding. Delirium could be a synonym. Therefore, encephalopathy itself tells us that the brain is MALFUNCTIONING in thought processes. Although it's certainly possible for circulation problems to COEXIST with the encephalopathy it's not necessarily its CAUSE.