Yes indeed, anonymous! Practically anything that can be tamed can be considered a pet, even fearsome pokémon such as gyarados. The trick is giving your pets the appropriate amount of care and space to maintain their mental health—as well as, of course, ensuring that they remain calm and docile around human beings.
In your metang’s case, it seems that it’s very comfortable around humans, so if you have enough space to keep one, it can certainly be your pet.
The Pokédex According to Bill 