Is it possible to sort, group and limit efficiently in Mongo with a pipeline?

Given Users with an index on age:

{ name: 'Bob',
  age:   21  }

{ name: 'Cathy,
  age:   21  }

{ name: 'Joe',
  age:   33  }

To get the output:

[ 
  { _id: 21,
    names: ['Bob, 'Cathy'] },
  { _id: 33,
    names: ['Joe'] }
]

Is it possible to sort, group and limit by age?

db.users.aggregate(
   [  
      {
        $sort: { 
           age: 1 
        }
      },
      {
        $group : {
           _id : $age,
           names:{ $push: '$name' }
      },
      {
        $limit: 10
      }
  ]

I did some research, but it's not clear if it is possible to sort first and then group. In my testing, the group loses the sort, but I don't see why.

If the group preserves the sort, then the sort and limit can greatly reduce the required processing. It only needs to do enough work to "fill" the limit of 10 groups.

So,

1. Does group preserve the sort order? Or do you have to group and then sort?
2. Is it possible to sort, group and limit doing only enough processing to return the limit? Or does it need to process the entire collection and then limit?