I don't know if it would. For overlays I don't stress the lamination that much, and I can't see it happening unless you fidget with them or something. Personally I have the overlays stored in a binder, and I only pull them out for the scenario, so there's very little stress. For cards if you shuffle them the traditional way you might be able to put enough stress to cause them to separate.
That said, the plastic used with heat lamination is thick enough that it is somewhat stiff. You may be thinking of plastic that rolls back from the edges. I do have some of that with the LFT Rat Chart cover page, for example. But the plastic there is thinner, more near plastic wrap, and the paper thicker. I have never seen that with anything I have laminated, but again I laminate over the edge, so I don't have paper exposed on the edge. This will also depend on the thickness of the lamination pocket. My laminator will accept three mil to six mil thickness lamination pouches. An ordinary piece of paper is roughly three mil thick. Three mil lamination is fairly stiff, and six mil is nearly rigid, partly because the listed thickness is per side, i.e. with a three mil pouch you end up with a nine mil output, three for the paper and six for the two layers of plastic. I use three mil, again because overlays are not stressed very much. I don't know for sure, but I think the plastic on something like the LFT Rat Charts is less than one mil thick, more a coating, and the paper is more like cardboard to give it thickness. And my Rat Charts are used more and more roughly too.
If you are protecting something like cards and you shuffle/flex them, I think you are right after some time they may become worn. That's a good reason to scan and print copies.
JR