i have hauled 16ft canoes laying both upside down and upright on the factory racks. I recommend getting a J-type kayak hauler that mounts directly to the rails. The universal fit rack mount right up with 4 bolts apiece. I currently use these and leave them up all summer. They fold flat when not in use and can still put a canoe on top of them. Here is a pic with a 12ft and 10ft kayak ontop, two straps apiece.
To answer your question, yes you can haul a 13ft kayak on the factory racks without anything but i would recommend the foam pads so it doesn't scuff or the j-type hauler.
Link to model in picture.
https://www.dickssportinggoods.com/p...3n1kykcrrrxpsr
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MINE - 97' SR5 manual (Desert Dune Metallic)
HER's - 14' limited (Altitude Black)