SQL Order By Clause Execution
===

This question isn't about order of executions. It's about just the ORDER BY.

In standard execution is:

- FROM
- WHERE 
- GROUP BY
- HAVING
- SELECT 
- ORDER BY
- TOP

Now supposed I have a statement like this:

    DECLARE @dt18YearsAgo AS DATETIME = DATEADD(YEAR,-18,GETDATE());
    SELECT
      Customers.Name
    FROM
      Customers
    WHERE
      Customers.DateOfBirth > @dt18YearsAgo
    ORDER BY
      Contacts.LastName ASC, --STATEMENT1
      Contacts.FirstName ASC, --STATEMENT2
      (
       SELECT 
         MAX(PurchaseDateTime) 
       FROM 
         Purchases 
       WHERE 
         Purchases.CustomerID = Customers.CustomerID
      ) DESC --STATEMENT3

This isn't the real statement I'm trying to execute, but just an example.
There are three ORDER BY statements.
The third statement is only used for rare cases where the last name and first name match.
My question is, if there are no duplicate last names, does SQL Server not execute ORDER BY statements #2 and #3? And, logically, if there are no duplicate last name and first name, does SQL Server note execute statement #3.

This is really for optimization. Reading from the Purchases table should only be a last resort. In the case of my application, it wouldn't be efficient to read every single "PurchaseDateTime" from "Purchases" grouping by "CustomerID".

Please keep the answer related to my question and not a suggestion like building an index for CustomerID, PurchaseDateTime in Purchases. The real question is, does SQL Server skip unnecessary ORDER BY statements?