Can polyuria due to diabetes be just nocturnal and/or only after pooping?

No: Polyuria in diabetes is due to high glucose levels. High glucose induces thirst and high intake of fluid leads to increased urine output in otherwise normal kidneys. The high glucose also is filtered into the urine and exceeds the ability of the kidney to resorb the total amount of glucose. The excess glucose in the forming urine acts as a diuretic preventing retention of fluid from the urine.