According to Bulbapedia, the move Curse has not been used in the anime.
As for the reason for it not being used, I would say that it is not an issue of it being too graphic. I would say it is that it's effect doesn't really fit into how anime battles usually go. Stat boosting is rarely seen, and the Ghost type affect also wouldn't really be fitting for the anime. How would it show that it has done damage to itself? And then how do they show the Curse doing damage to the foe? While these effects can be taken for granted in the games, the anime requires an actual full-blown image.