No, that would be incorrect. The games have the ability for all of the Pokemon games to have every Pokemon in exitence up to whatever gen the game is, making everything infinite. But the Pokemon you trade and recieve has nothing to do with the Pokemon story.
Sure, it's possible to fill your PC with 100 Arceus is you want to, but whether it was hacked or traded.. it still doesn't effect the storyline of the games. If I were to make my own Pokemon generation and game and completely make a legit story that fully matches the storyline of other Pokemon games I'd be sure to make cool Pokemon that there would only one of, but if hacking or trading you can get as many as you want. Does that mean I made the storyline of the game so that all of the Pokemon from that generation are infinite?