Predator drones have enough payload to carry several AIM-120s (where to mount more than one is an open question), which is a ~40mi range fire-and-forget air-to-air missile. Whether the F-35's stealth/avoidance is good enough, I don't know. But if you had say a dozen drones patroling an area, I don't know if I'd want to take an F-35 nearby.
So no, I don't think drone tech is good enough to down F-35s, but I think with sufficient zerg tactics, it could deny airspace.
So no, I don't think drone tech is good enough to down F-35s, but I think with sufficient zerg tactics, it could deny airspace.