I was looking at that the other day. I was impressed with the idea, but I have to wonder if it will fly.
I can admit that back when I was getting started in turkey hunting I had one shotgun. It was a Rem 1100, and I got a collection of barrels for each sport I used it. All told I had 4 barrels. Skeet, trap, Deer slug, and upland. One, the full-choke trap, doubled as my turkey barrel. I would put a camo sock on the stock and receiver when I went turkey hunting to camoflage it and tape the barrel.
This is kind of the same idea. However, over the years, I got tired of all the changeouts. The first thing I did, when I got the scratch was by a Mossy 500 to be a dedicated turkey gun. I got it all camo'd up and left it that way. The 1100 now sports nice fancy walnut and it stays by my bed with the deer barrell in case something goes bump in the night. A few years later, I managed to snag a rifled slug barrel cheap, so my turkey gun also became my dedicated deer slug gun.
On the other hand, I don't know many people that really NEED a stockless, pistol grip shotgun, and if they do, they probably need it all the time and don't need to be messing with stocks and forends.
Bottom line: If I was starting out, I might really think about this TLS system. However, in short order, I'd probably go out and get myself a second gun. A dedicated turkey gun makes sense, as does a dedicated slug gun for deer.