Invincible? From everything I’ve seen, no. Frostmourne is just really powerful and is able to share that power with its wielder.
As I’ve mentioned the last time a similar topic came up surrounding Deathwing and Elementium, nothing is indestructible.
Every substance has a melting point, a sheer and tensile strength, and a molecular and nuclear bond strength. Exceeding any of those will damage or destroy it. If magic somehow makes it invulnerable, then what happens when that unstoppable force/immovable object meets its counterpart? It devolves into wand-measuring, a comparison of who’s magic is more magicky, and that never goes anywhere.
Even then, even if you still want to fall into the trap of claiming something is “indestructible” or “invincible,” there’s still the issue that it may not protect you. You can easily be killed through “indestructible” armor is someone hits your helmet hard enough – the blow will smash your indestructible helmet through your very destructible head. Heat will seep through the armor and roast you alive inside it. Acid will get in the chinks and dissolve your flesh, or release noxious fumes that kill you if you inhale them.
There is no such thing as a “perfect defense.”
If an Ultralisk stepped on Arthas, or if a Baneling or Roach managed to soak him in acid, or if a horde of Zerglings dogpiled him and bodily ripped him apart, or if a Glaive Worm burrowed through one of those many chinks in his armor, his body would be destroyed and he would die. His armor and wards would not be able to protect him from those things.