Can a GA magneto-spark plug ignition survive an EMP?
Can the coil and capacitor (condenser) magneto/spark plug ignition
  system as exists on most general aviation aircraft survive an EMP?


Like anything it depends on the EMP's strength, the angle of incident to the device and the device in question. The various things in an aircraft will break down for different reasons. But for the rest of this lets assume an EMP that is sufficient to fry stuff. A magneto will suffer toasted coils as the induced current could potentially generate enough heat to degrade the resin coating on the wire they use on coils. It should however be noted that the magneto is more than likely shielded to prevent interference with avionics which will play out in your favor here.  


  How about most turbine engines? I'll use a PT-6 as an example. I
  assume the FADEC would be toast?


Most likely yes. Again the unit is generally housed at least in some capacity in a shielded case but modern PCB components don't play nice with large induced currents. Turbines do have an Igniter system that may see some damage depending on the severity. 


  How about other parts of the electrical system such as the battery? 


Things like interior lights will most likely blow out, batteries (depending on type and casing) could go. Overheating is a concern if enough current is forced over the line. 


  Is there any data or research on this?


There is some Mil-Specs (MIL-STD-1541 (USAF)) out there that cover it for the military. This question covers it for airliners. You can find at least one book on the topic here. There was a lot of research on this that pertains to missile systems as one anti-missile defense was to detonate a nuke in front of the oncoming unit. If the blast did not take it out the resulting EM field would fry what ever guidance and control systems were on board (assuming it was not ballistic). As such, work went into making the units EMP hardened. I'm not sure that work is very public though. The soviets were big users of vacuum tubes as they believed them to be far less susceptible to EMP's. It looks like this company does testing and research on EM hardened aircraft.