I think so. It's wide, just not very deep. It will hold a can of chicken noodle soup, but not a can of spaghetti and meatballs (which has a bigger can). I do think you would be able to put the yogurt cup in it. I'll try it tonight and let you know! UPDATE: I tried this myself tonight with a 6 oz. cup of yogurt. It is deep enough, but not wide enough. The top of the yogurt cup won't fit at all. Not even by squeezing. Sorry, but this will not work.
No, I don't think so. If it's wide enough for the whole container to fit, I don't think it's deep enough. I think the yogurt cup would be too tall to screw shut. It would be plenty big enough to pour the yogurt into it though.