Asmat
I would not be so concerned about those carbon battens. I would rather consider the mast, which you cannot reef away in a thunderstorm. Even an unstayed and not-conducting mast, made from dry wood or GRP, will have its tip on ground potential if it is equipped with a weather station or masthead light. Such a mast certainly would benefit from a real (25mm2) lightning conductor.
I also wonder, since so many yacht rigs often are more or less covered in salt spray, that also the wood/grp mast top will be at ground potential, even with no wires running up the mast. Therefore it would make sense to fit a lightning conductor, anyway.
The problem with carbon masts is that they are conductive enough to attract lightning, but have way to much internal resistance to lead the current to ground. It is therefore likely that they will be damaged by the heat, when struck, since the epoxy is not very heat resistant.
I wonder how the makers of carbon fiber (composite) aeroplanes deal with this. Any suggestions?
Arne