A dealership with that kind of info? I doubt it. Probably a publicity stunt. I also don't think Porsche would give the Cayman the 4 liter.
Not so sure. To my knowledge, Porsche hasn't yet denied dropping a six into eventual GT-spec 718s. As @VXR notes, the 718 isn't an entirely new platform (more of an elaborate facelift), so slotting in the same 3.8 as before is far from being impossible.Absolutely zero chance of a 4.0l Cayman.
The 718 has been designed ground up for a flat 4 turbo. Engineering it for a NA flat 6 would be a huge and uneconomical task.
Plus Porsche have the 991.2 GT3 and GT2 (RS) to launch, so any GT 718 will be a long way off. And when it comes, it will have some sort of 4cyl turbo motor (maybe twin turbo, maybe more capacity, but not a NA flat 6).