360 km/h is 200 knots, which is above the V1 for airliners. That makes it more feasible to chase an airliner on takeoff to try and get sucked into its engine, than to just hope it runs into a slow drone. However, this speed is only special for a quadcopter, fixed-wing drones could do this for decades.
It's possible that a major proliferation of drones could lead to major urban airports eventually adopting the same drone-jammers as used by military airfields. But it will probably have more to do with preventing accidents from amateur photographers than with anti-terrorism.
Reducing the RCS of a drone is not as easy as it looks. It might be small, but a single metal screw has sufficient RCS to be spotted by radar at close range, and drones also have motors and antennas. Since they are only effective during takeoff, they'll be at very close range to the airport's radar. A stealth drone will need advanced materials, shaping, and LPI electronics, making it cost as much as a missile.
In a military scenario, a more effective tactic is to load small drones with explosives and try to fly them into anything flammable. They are not effective against fast-moving targets, but aircraft on the ground make for easy targets. Drones "bird-striking" an engine is a concern in civil settings because explosives are hard to get for a civilian.