They use a peltier cooler and do work, it takes a while to cool down however. Most people expect to plug it in and have stuff cool down instantly. I use the peltier cooler out of one on a box about 6" x 6" x 8" to cool down a digital camera while doing astrophotography and I can get it down to 20-25F on a 90F night "IF" I leave it on for 2 hours to reach that temperature.
If you want to use the same thing in something else you can search ebay for peltier coolers of varying sizes and put them in anything.
You can read this PDF that will tell you how long it will cool and how much it will draw on a battery at what temp in a nice chart for the 16quart cooler. I imagine the 40quart one is exponentially a bigger battery drain.
http://r1.coleman.com/Manuals/3000000540.pdf
Personally unless you have it plugged into your car while traveling it's not going to work because they are a big draw. Get a good cooler or build a better cooler and you can keep ice for up to 5 days even down here where it hits 100F during the day if you keep it shaded. Or get a refrig that will run off propane.
I personally use a yeti cooler but that would definetly blow your budget out of the water but it's great when offshore fishing or elk hunting and can keep 2 quarters of an elk on ice for up to 7 days or keep ice out on the gulf for 3-4 days easily in 90-95F heat. I wouldn't spend that much on a cooler just to go "camping".