If you practiced assiduously with it it would probably be a good weapon for harvesting small game. But I would point out that in the space it takes to store a slingshot, extra bands and some suitable ammunition you could simply carry a PLB and not need to hunt in the first place! While I'm being a bit facetious, conventional wisdom holds a pretty low place for hunting & fishing in survival kits. Food is seldom a high priority since you won't generally live long enough to starve to death. I can think of a couple fairly high profile cases where the person was lost long enough for food to become an issue but I'm not sure a slingshot would have helped.

My take is that it doesn't hurt to have it in your pack if you're proficient with it but I'm not sure it's the best use of space if you're talking just survival gear.