Does hitting a creature with a magical creature counts as magical damage?

Half-Orc Barbarian Conan has been Enlarged, making him Large. During a fight against some Couatls, he managed to grappled one and beat it to death.

Now, having already something (the body of the dead Couatl) in his hands and being a tad affected by its current rage, Conan decides to strike a second Couatl with the first one. Laughs all around the table as the DM rules that he can indeed wield the corpse as an improvised weapon (bludgeoning), given the situation.

A Couatl is immune to non-magical bludgeoning, among other things. But given the fact that the first Couatl is a magical creature and has the Magic Weapons feature, does the damage counts as magical damage?

Magic Weapons: The couatl’s weapon attacks are magical.

If yes, would any “magical creatures” work for this purpose or only ones with the Magic Weapons feature?