Yes, broken windows are covered by accidental damage insurance but only when it is added to your building insurance policy. Other events covered include:
Accidental damage to toilet basins, sinks and other bathroom fittings
Damaged drains, pipes, cables and tanks connected to your home
Cracked wall tiles
Damaged kitchen units, including accidental damage to built-in appliances like ovens
Any unintentional hole in a wall
Flood, fire, storm and other water damage
Collision damage – from a car, a tree or other forces – to the building