Yes, they can. Where required, crew may inform the passengers through an announcement that PEDs be switched off due to flight safety requirements. Passengers must always comply with safety instructions.
Note that effective 21 March 2017, in accordance with new US government regulations, all passengers travelling on United States-bound flights are prohibited from carrying any electronic devices on board the flight other than cellular and smart phones and medical devices needed during the flight.
Qatar Airways has made special arrangements to assist passengers in securing their devices in the aircraft’s baggage hold. Prohibited devices, including laptops, tablets, DVD players and electronic games, must be carried in checked luggage only.