No, the Death's Shadow will be put into your graveyard for having 0 toughness as a state-based action before you get priority to cast a spell.
January 9, 2017 3:11 p.m.
Death's Shadow will die before you can save it. State-based actions are checked any time a player would receive priority. They check for things like creatures having more damage marked on them than they have toughness, creatures with 0 or less toughness die, etc.