The anime not happening could have been both a good thing and a bad thing.
The downside, as people have already said, could be the fact that Pokémon would have been a rather obscure franchise, and not end up as popular among gamers as it is today. But then, obscure games can very well make it by word-of-mouth.
However, I think that remaining in obscurity would be tons better than the rep it has now. In the collective consciousness, Pokémon should have been put on the same shelf as other classic franchises for all ages by Nintendo. Instead, thanks to the anime, it is widely considered by people not in the know as a game that no self-respecting person over twelve should play, because certainly it's all cute critters, Pikachus, singing Jigglypuffs, comically inept villains, and cheesy messages about friendship from start to finish. When I talk about gaming in public, I can freely admit I play Mario, Zelda, Sonic... even Kirby! But never Pokémon.
So here. Without the anime, the game could have become a much more respected franchise on its own merit, it would have been more difficult, but in the end result it would have a much better rep. Instead, it is something I must keep as a guilty pleasure to avoid a potential social suicide.