“Adhesive Explosive” activates its effect as soon as it’s flipped face-up. So if “Mystic Swordsman LV2” attacks it, its effect will not activate, but if “Drillroid” attacks it, its effect will activate.
If this face-down card is attacked by “Horus the Black Flame Dragon LV6” or “Guardian Kay’est”, it will still be equipped to the attacker, but it will not destroy the equipped monster during the Standby Phase.