Would it be a positive thing if schools created a special group for lonely kids?

There are so many kids that sit by themselves at recess and lunch-time every day at school. Would it be a good idea to create a group that kids could join at lunchtime? I ahven't quite figured the mechanics of how it would work yet. Do you think these kids would be bullied or teased cause they were in a group like this? What would be the pros and cons of creating such a social group. I know it would need to be supervised somehow...Any ideas and suggestions would be awesome. Thanks heaps. I'd love to hear from teens especially but all answeres are much appreciated.