No, after your opponent discards his evil character in this scenario he still has a multitude of options to extend the battle:
He can add a character to battle via Unknown Nation, Gates of Hell, Madness or A face down EC via site guard
He can play a dominant to remove the soul from play (Son of God, Burial)
He can play a dominant to remove the Hero from battle (Christian Matyr or Grapes of Wrath if there's a placed EE on the Hero)
He can remove the Hero from battle via Artifact (Unholy Writ, Magic Charms)
He could even extend the battle phase by playing another dominant i.e. Mayhem or Falling Away, to either hope for something else to play, or to remove a soul so as to not end the game.