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.
First it has to be directed in the right direction. Need a good radar system somewhere for that. It also has a much higher hit probability against a target, especially a distant one, if you can send it remote course corrections. Note that neither of these need to be on the launching platform, but they need to be somewhere in the local area.
If every Predator gets a 100W wideband transmitter and SOME of them get instead of weapons the equipment necessary to process the reflections and do the calcs then the others can get that target information and blammo.
If there are 100 Predators for every F35 in the combat zone and they ALL turn on their transmitters simultaneously at some kind of interval you're never going to know which one is carrying weapons and which one is command and control. So you can't do prioritized targeting and thus you're shooting blind. Yeah you can shoot down some of them but once you're out of missiles that's it.
Do we have to worry about 3rd world countries being able to muster this kind of response? No. But there are plenty of industrialized countries that could, and they could bleed us dry one $200mm plane at a time.
A hundred drones could at least take out all the airport runways, leaving it nowhere to land...
Nothing says you can't have a few dozen/hundred drones with SAMs, either.