When Kog'Maw dies in combat, does the unit heal before the Deathknell trigger?

Yes, units heal from combat damage before Kog'Maw's Deathknell trigger resolves.

According to the official rulings for Kog'Maw:

1. Combat Damage is dealt: Units take damage based on Might.
2. Special Cleanup: Units that have lethal damage (including Kog'Maw) are identified. Kog'Maw's Deathknell trigger is added to the chain as a pending item.
3. Healing: All units heal from combat damage during this cleanup step.
4. Resolution: After healing is complete, players have an opportunity to react to the Deathknell trigger on the chain. Once the chain resolves, Kog'Maw's Deathknell deals 4 damage to all units at that battlefield.

Because the healing occurs before the Deathknell damage resolves, Kog'Maw cannot kill a unit with 5 Might using only the 1 damage he dealt in combat plus his 4 Deathknell damage; the unit will have healed the combat damage before the Deathknell damage is applied.

Reference: FAQ entries regarding Kog'Maw's Deathknell interaction with combat cleanup and healing.