I am sure it could be done but why would you want to. If you get a decent fish on you would have to kite back to shore making the caught fish a live bait for something bigger with big teeth. No thanks
Probably could take the bait out (and line ) for a mate on shore further out than available for casting and drop it of
And add more strings to get tangled up in?
Can see you losing a toe or two when u get snagged on the ground.
Or is this just another troll.
Someone in Botany got hooked while kiting by a fisherman trailing a line behind a boat.
Then again it was in the deep dark ages of kiting so I forget who it was... 
Lol thats funny
I think you should try windsurfing if your getting bored of kitesurfing and you feel you have to go fishing.
Why not try dangling a net from the kite as well and see if you can snare a mutton bird while you are at it ?
Why not tex-screw a flower pot to the front of your board and trying growing tomatoes while you sail along ?
Why not carry a rifle and see if you can down a gazelle whilst boosting big air ?
If you went windsurfing your board would be big enough to light a fire on the front and you could have yourself a roasted garfish, mutton bird and gazelle sandwich with a tomato side salad.
(roasting a gazelle on the the front of your kiteboard - that's not living)
