Yes, it would do damage to the zombie. The reason for this is that in a case like this when a card is damaged/destroyed if it or another card has a reaction in response to this resolution on the current card stops until the second card is finished.
So what would happen is 3 damage is done to the cultist killing it. This triggers the ability that adds a zombie into the field of play pausing the ability that does 3 damage to all non hero targets until the zombie is in play. Once the ability that is doing the damage resumes there will be another target in play for it to damage.
This is important for a similar situation with ae damage and a card like the sonic mine that damages hero cards and prevents them from doing damage. When it dies it will prevent the rest of the AE damage from happening.