Simply put, it would be fine. Things would actually be better than they are now.
Think about it for a few seconds. There are very, very few games that within 6 months of release aren't pirated and cracked. There are even a few that are ready after a week or two.
The only major players in consideration here are the people like we find here, who'll think about their purchases and buy things to stay in line with their rights, or because they're willing to wait rather than play now. Most other people will simply see the advertising, and buy it.
You have a number of conscientious consumers who will look out for the company, and a number more who will buy it, rather than just ignore it, because they don't see it having some crap like GFWL [Which is an instant 'don't touch this game' for me].
So, your sales will remain about constant, or go up.
Piracy will continue, but it won't be as prominent, as you'll have made it easier to get into your game. Yes, people will still pirate the shit out of it. You can spend a fortune on principal trying and failing to stop them, or you could just let them do it, and save yourself a lot of money on DRM - another fact that shows the creators better off financially if they didn't use DRM.
Overall, DRM is a flawed practice. It doesn't work, and its an act that attacks people. It makes it inconvenient for your true users to use your product, and the pirates will take it as a challenge as you're trying to stop them.
A better practice would be to constantly update your game with new, exciting and interesting content for free, for legitimate copies of the game [Minor DRM, nothing intrusive. A CD key and online registration is it]. What this means is that legit players are rewarded, constantly getting new content easily, whilst its likely that pirates will need to re-download the entire game to install these patches, which is inconvenient and many won't bother. It becomes a war of convenience, like it is currently, but you're the more convenient option. This means you'll win the war, whereas presently piracy is a appealing option for many as its free, and more convenient than playing a number of games legitimately.