In 30 years, I've never seen a chunk of plastic come off a new drive like that, esp one brand new (very very old drives in hot areas might have some plastic brittleness). I'd almost be tempted to try your luck with a warranty claim. In my view you'd need quite a considerable amount of inappopriate force to break off a piece like that. 

I am obviously not privy to your installation mechanics, but I am assuming you didn't throw it from the other side of the house like you were trying out for the NZ Olympics Track and Field team, then that little force should not have broken that bit off like that? 

The connectors will have a matching sized recieving connector, and it should be fairly obvious as it gets inserted if it's in, as the drive would line up identically to the other one and there would be a clear 'acceptance' sound/feel. 

The screws on the side could help guide you too. I am unsure on your specific model, but if the screws could be partially inserted so the drive could move back and forward, that would almost certainly assure connector link up.