Not always...There is another aspect to sport fighting which I think is often overlooked.
When you roll (everyone knows I'm a BJJ guy right?) with someone who trains like you do, they know many of the techniques you are going to use, and they know how to defend against them. In consequence, you are forced to train different ways of setting techniques up and applying them, because if you just go for it against a person that is not only resisting but knows what you are trying to do, chances are you are going to fail. That type of experience just makes your techniques that much stronger when you go against someone that doesn't necessarily know how to defend against your techniques.
For example, if a Judoka gets really good at performing throws against other judokas, I like his chances of being able to throw me if we meet on the street.
That, and I think that sport fighting goes a long way in removing some of the nerves that are involved in a real fight. And I think that nerves are a lot more important than many people realise.
It can also set up the "you attacked me the wrong way" situation. Lots of the knife and tappy-tap stick work out there is a good example; they're training tricks and tactics that will only work against each other, and are overly complicated for a "real" situation. Or the student gets so tied up trying to trick and pull off techniques against people who know what's coming or work on particular motions or habits that they aren't practicing solid principles.