tozmo1, I have not used any of the products from the slate-lite firm. It was just the first example that I found on the internet to illustrate what I was talking about. I have used a similar thin slate from another company. It was years ago, and I don't remember the name.
One problem that I encountered was the condition of the material when it was shipped to me. I bought 2 feet x 4 feet long pieces (5 in a pack), and the corners of some of the sheets were damaged during shipping (or sent out that way by a company trying to pull a fast one).
I used liquid nails to glue the sheets to a cabinet that I was refinishing (it had panel sections on it that I covered, so it added a lot of pop) and I also glued a rectangular piece to the front face of my stainless steel laundry sink to dress it up. I also used strips of it as part of a soffit design above a sink.
Relative to what you are proposing, I think the product that I used would have been able to stick to the curves on the top side of your table, but it might have a problem with the more intense curves on the inside of the piece (assuming your plan is to entirely cover it). Where I definitely think the product that I used would have a problem was the curve that the piece rests on. The weight of the table would probably cause that section of thin slate to crack. What I would do is run the thin stone all the way down to where the piece rests on the floor and then leave a small (1 inch?) strip of the table uncovered where it rests on the floor. Since it is facing down, no one would see it, and you could always paint that small strip the same color as the thin slate (or fill it in with wood putty to make it level with the thin slate) if you thought it might be visible. Because the material (at least the one I used) has a rough surface (like sand paper), you probably would not want that material touching your floors anyway (especially if they are wood) because it could scratch them when the table is moved around. You will need a lot of clamps to make it work unless you use some sort of instant glue or contact cement. The problem with contact cement is that you only get one shot at matching the pieces up. With liquid nails, you can play with it to make it fit properly but then have to clamp it.
Cutting the thin slate is a concern. I used a dremel to cut it. A box cutter is not going to work on this stuff.
The edges of the thin slate (at least the product that I used) are another consideration. The edges show the backing material. I used Schulter tile edging to hide the edges on the projects that I worked on (think of a picture frame--I butted up the edges to it).
Q