Will the Messiah revive the dead bodies during the messianic age according to Judaism?
According to the Rambam this is not necessarily true, see MT Melachim 11:3
One should not presume that the Messianic king must work miracles and wonders, bring about new phenomena in the world, resurrect the dead, or perform other similar deeds. This is definitely not true.
So even if resurrection of the death is a fundamental tenet of Judaism (see Maimonides' 13 principles of faith), it might come at a later time.