TCG
If a Mermail Abyssturge discards an Atlantean monster for the cost of its effect's activation, and then it targets that same Atlantean monster to be added back to the hand, that Atlantean monster will have it effect triggered, and it will activate after Abyssturge's effect has finished resolving.
OCG
In the OCG, the discarded Atlantean monster does NOT trigger, and it won't activate after Turge finishes resolving.
If a Mermail Abyssturge discards an Atlantean monster for the cost of its effect's activation, and then it targets that same Atlantean monster to be added back to the hand, that Atlantean monster will have it effect triggered, and it will activate after Abyssturge's effect has finished resolving.
OCG
In the OCG, the discarded Atlantean monster does NOT trigger, and it won't activate after Turge finishes resolving.