Is a sort faster when the data is already sorted?

Whenever SQL Server needs to sort a data stream, it will use the Sort operator to reorder the rows of the stream. Sorting data is an expensive operation because it entails loading part or all of the data into memory and shifting that data back and forth a couple of times. The only time SQL Server doesn’t sort the data is when it already knows the data to be ordered correctly, like when it has already passed a Sort operator or it’s reading from an appropriately sorted index.

But what happens if the data is ordered correctly, but SQL Server doesn’t know about it? Let’s find out.