could a laser weapon...onboard such a drone be accurate enough to do significant damage as to take one down?
These handheld lasers have never taken down a singe airplane, IIRC, due to multiple backup systems starting with a second pilot not likely to be simultaneously injured and the fact that most large airliners use instrument landing technology and can be flown with no visibility outside the aircraft.
Land-based laser pointing at airplanes in landing approach zones is arguably even more effective that air-mounted laser pointing on a UAV, I would expect.
Think of that restaurant in Denver where people can see the incoming planes lined up for 50 miles approaching the airport. Any malicious laser-pointing terrorist or creep can use any promontory to attack the cockpits in incoming planes without needing to mount the laser on a UAV.
UAV/drones are much more effective against aircraft turbofans as a kinetic weapon with no onboard lasers or explosives needed, IMO.