Index usage in group stage?

I have the following query
db.collection.aggregate([{ “$group”: { “_id”: { “TerritoryId”: “$TerritoryId”, “CustomerId”: “$CustomerId” }, “TotalDue”: { “$sum”: “$TotalDue” } } },
{ “$sort”: { “TotalDue”: 1 } }])

and index defined as follows

{ CustomerId: 1, TerritoryId: 1, TotalDue: 1})
I noticed by viewing the execution plan that the index is not used. I was wondering way?

How about updating the index to {TerritoryId:1, CustomerId:1, TotalDue: 1}?

Don’t feel $group will use index though, as the engine needs to fetch all the documents anyway.