Does the Metal Mario outfit do anything special in Super Mario Odyssey?

It's hard to prove a negative, but no, the metal cap doesn't give you any bonuses, buffs, or unlock any additional moons. It can quickly be proven that it doesn't change your swimming physics or make you invincible as it did in Super Mario 64.

The cap and suit are unlocked for 1000/2000 coins when you get 560 moons which should be well after you've unlocked all of the areas in the game. The only outfits that allow you access to secret areas are the ones which are bought using local currency.