No, this isn't possible.
Possibility Storm says the
maycast the spell that shares a type with it. While the restriction by
Eidolon of Rhetoric says they can't, after the elect to not cast it every card exiled will be returned to the bottom of their library.
All this interaction does is lock the board at it's current board state until a side draws
dead, or either component is dealt with through something existing on the field. You'll need
Jace, Memory Adept or Keranos on the Field first to ensure the win.