If the pitot tube was completely blocked air tight then it would carry that pressure for the entire flight as it would not leak out ie surface pressure would be retained where as if it was simply obstructed it would be unable to measure dynamic pressure and the higher surface pressure in the system would release as the aircraft climbed. Largely academic as indications would be grossly in error either way.
GPS ground speed readout with an allowance for wind is a good back up.
Does anyone know if fuel was dumped as an immediate return to BNE would result in an overweight landing unless dumping took place. No accurate airspeed indications would greatly complicate the overweight landing checklist when configuring.