No, gap insurance does not cover your engine for damages due to the timing belt breaking. GAP insurance is used to cover the difference between what is due on a car and the actual cash value if a new or leased car is totaled before the balance of its loan or lease is paid off. Again this insurance kicks in if the vehicle is declared a total loss by an insurer and thus is considered a "covered loss," not if you have mechanical issues that are not covered by your primary insurer.
Coverage for specific parts of your vehicle, such as the engine or transmission, to be repaired or replaced is usually done with by means of a warranty. Warranties can be purchased at dealerships, financial institutes or online. Some financial entities also offer mechanical breakdown insurance.
With a normal auto insurance policy neither collision nor comprehensive covers mechanical problems, such as engine failure, that is not related to an accident that would be covered by the terms of your policy. If your car is not covered by your primary insurance company for the actual cash value (ACV) of your vehicle then your gap insurance would not be activated.