The gimmicky "survival" .22s look cool, but I don't think they really do much to warrant going that route. The Marlin Papoose is a pretty good little gun, but for my money the Marlin 795 brings more to the table. Sure, it doesn't break down and store away, but the 795 is a little gun to begin with.
As I'm sure you know, there isn't much to a .22 rifle. The barrel and action are pretty light, factor in a plastic stock and the barrel only be 16", it's a sub $100 gun that I can throw in the truck when I hit the range, or one that could be indispensable should I need to bug out. a 500 round box of .22 and the 795 with a few preloaded magazines could net me a lot of small game.
That said, if there could be only one rifle in a survival situation, as in "the house is coming down around our ears, the sky is as blood, head to the hills and may God be with ye so grab ONE gun and run" it's really tough to beat the AR platform. While not as cheap to feed as a .22, cheap plinking .223 can be had for sub $5 per 20 rounds, and even that ammo has plenty of oomph for game and defense.
An AK is another gun to consider, but if you are talking about a "worst case scenario" where you may need to feed you gun off what you find, .223 out saturates 7.62x39 in the US...but that's getting a little too tin-foil-hattish for my taste.
In short, a cheap lil .22 is never a bad thing. If you want one with a survival flair, go for it. They sure look cool. However, I think a 795, Model 60, or 10/22 (if you want to pay a bit more or customize) is a more practical bet. If you want something that can help you "survive" both by getting game and offering enough personal defense firepower the AR platform is a good one. If you want a robust beater, it's tough to beat the AK.