Natural fiber string on a kite, probably wouldn't last long before the electricity burned through the string breaking the path to the ground. Monofilament fishing line or synthetic twine might be different. It all happens so quickly and a wet string presents a bigger risk than a dry one.
AC current is super dangerous. It can lock your muscles so you can't let go. Then there is the effect of AC on your heart rhythm. The take away is that no one should be anywhere near live current in this country. You have to test every time before you touch a wire just to be sure as really weird things are done by "electricians" here all the time. Turn off the current, make sure someone can't come along and turn it back on. Test, and test again. House wiring scares me. I won't go near power lines. Better to buy a new kite.