Actuall, the cage in that pic looks like welded, tubular steel. if it's welded to the floorpan, and not bolted in, it would be functional. don't think that bottle holder is safe, though.
A cage will stiffen up the unibody big time, less likey you'd flip the car, since it will be more solid, flex less, and will handle better once installed.
what makes monkey bars unsafe is that the tubes are only slip-fitted togeter, and the cage itself is merely bolted to the floorpan. this will stiffen the chassis a bit, but not make the car much safer. if you weld all the slip fittings and actually weld the cage into the structure, it will provide the safety too. coures, you need to strip the paint to do that, and then you'd need to repaint it once welded.
Cheapest soution, go to a welding shop and have them weld up a custom cage, paint it (except the feet of the cage, of course) have it welded in, will cost you much less, and it's custom fit to your application.