Despite the fact that e-mail has yet to be introduced to the fictional realm of Pokémon, and no such thing can be interacted with it in the games, there have been a few Pokémon introduced that can exhibit the ability of transferring themselves through the internet, and by extension, e-mail services such as Gmail. The most clear of which being Porygon, which Pokedex states:
A Pokémon that consists entirely of programming code. It is capable of moving freely in cyberspace.
Cyberspace is defined as the theoretical environment where communication between computers occurs, which includes electronic mail. As Porygon can travel through it, cyberspace in fact exists in the Pokémon world, allowing our polygonal friend to travel the web through it, and by extension, e-mail! So while not all Pokémon can be transferred through e-mail, Porygon, and likely its evolutions, are exceptions to this fact.
