Is online drm actually reducing piracy?
No. In fact, even the best DRM software out there now can be cracked within hours of a game's release.
Don't pirated copies come with removal of online drm?
Yeah, pretty much.
I'm still a fan of how Stardock handled piracy and DRM for Galactic Civilizations 2. Before it was made available on Steam, there stance was they didn't care if people pirated the game, but they somehow worked it so only people who purchased the game could get the patches. Part of it was that to access the patches you had to input a unique code on their website that you received upon registering your copy after purchasing it. And since the original release was plagued with some pretty significant bugs (perhaps by design as an anti-piracy measure) even people who pirated the game were forced to purchase it eventually so they could get the patches necessary to make the game playable.