No, Kel'Thuzad was working for the Scourge before Arthas. Kel'Thuzad created the Cult of the Damned and distributed the plague that turned people into the Undead. Without Kel'Thuzad the scourge or forsaken would not have existed. Arthas as a human actually kills Kel'Thuzad in Andorhal and then once Arthas is corrupted by Frostmourne, Tichondrious, a minion of the Burning Legion and a Dreadlord, has Arthas gather Kel'Thuzad's remains and resurrect him. That's when Kel'Thuzad takes on the form of a Lich. Necromancers all practice and train in what Kel'Thuzad mastered, raising the dead.