My boyfriend an I have an interesting plan. We want to build a foam core fiberglass kayak, no woodworking or molds involved.
There are many who have built airplanes using a similar method. However I recommend that you DO NOT use the beaded polystyrene foam. It is far more flexible and much weaker than the rigid polystyrene that is used for airplane wings. The rigid foam is available in home improvement stores and is used for insulation. It is usually blue or sometimes red (pink) I think. If you want larger pieces, houseboat pontoons use a big block that is orange (at least the stuff I saw was).
The stitch-n-glue plywood boats are essentially the same kind of structure as what you appear to be thinking about. The difference is that wood is used as the core of the sandwich instead of foam. There are some advantages to using wood rather than foam. The wood is more dense and is stronger. This allows for a thinner fiberglass facing and probably a lighter boat. A higher density foam would also work like the wood, but styrene is not available in high densities (and the foams that are available in high densities will emit a toxic gas when cut with a hot wire).
I can relate to wanting to find a way to use your CNC foam cutter to make a kayak (I have two CNC metalworking machines). Just be aware that a stitch-n-glue kayak will be easier to build and likely a little lighter. I also understand that there are those that like making things with fiberglass and don't like using wood.
At any rate, your approach is certainly viable and a quality boat can be made this way. Boats take a lot more pounding than airplane wings (there are no rocks or beaches up in the air), so keep in mind the strength of the materials you are using....