The answer is yes - all birds have the ability to lay unfertilized eggs, however in the wild this is a rare occurrence due to the drive to mate.
The laying of unfertilized eggs is simply a method of disposing of the unused egg from the body of the bird.
The domesticated chicken and duck are unusual amongst birds due to the fact that they will lay an egg almost daily. This useful feature has been selectively bred into the domesticated species for hundreds of years, and is also partially due to the fact that their eggs are removed daily.
If a chicken or duck is left with their eggs, they will start to brood, stop laying eggs and try to hatch the eggs they already have.