Yes, protein contains calories just like carbohydrates and fat calories. All three sources function differently in the body, but if you consume more calories than your body can use, those calories can be stored as fat (that includes protein calories).
Just because it is protein doesn't mean you don't count the calories consumed. The reason carbohydrates can effect fat stores more so is because they effect insulin levels more than that of protein. Insulin plays a big role on metabolism, and if not managed properly, can lead to an accelerated rate of fat storage no matter what you consume. And of course fat is more likely to be stored than protein because it contains about twice as many calories as protein and carbs.