"When [...] would leave the battle area other than by battle" refers to when that Digimon is placed in the trash other than as a result of a battle, returned to the hand/deck, placed in the security stack, moved to the breeding area, or placed under another card.

No, it doesn't leave the battle area. DNA digivolution results in a digivolution into a new Digimon that is considered a different Digimon from the one that would leave the battle area.