In SQL Server, can I guarantee an order without an explicit ORDER BY clause when an index seek is forced on a table with only a clustered index?
Am I right that it will guarantee the order in this case without an order by clause?
  


No. A Flow Distinct that preserves order (allowing ORDER BY without a sort) is not implemented in SQL Server today. It is possible to do in principle, but then many things are possible if we are allowed to change the SQL Server source code. If you can make a good case for this development work, you could suggest it to Microsoft.


  
  If not, is there another method to force a plan that is as fast as Solution A, preferably one that avoids sorts?
  


Yes. (Table &amp; query hints only required when using the pre-2014 cardinality estimator):

-- Additional index
CREATE UNIQUE NONCLUSTERED INDEX i 
ON #Orders (StoreID, CustID, Amount, OrderID);

-- Query
SELECT TOP (500) 
    O.CustID, 
    O.Amount
FROM #Orders AS O
    WITH (FORCESEEK(IX (StoreID)))
WHERE O.StoreID = 1
AND NOT EXISTS
(
    SELECT NULL
    FROM #Orders AS O2
        WITH (FORCESEEK(i (StoreID, CustID, Amount)))
    WHERE 
        O2.StoreID = O.StoreID
        AND O2.CustID = O.CustID
        AND O2.Amount &gt;= O.Amount
        AND
        (
            O2.Amount &gt; O.Amount
            OR
            (
                O2.Amount = O.Amount
                AND O2.OrderID &gt; O.OrderID
            )
        )
)
ORDER BY
    O.Amount DESC
OPTION (MAXDOP 1);




(500 row(s) affected)

 SQL Server Execution Times:
   CPU time = 0 ms,  elapsed time = 4 ms.


SQL CLR solution

The following script shows using a SQL CLR table-valued function to meet the stated requirements. I am not a C# expert, so the code may bear improvement:

USE Sandpit;
GO
-- Ensure SQLCLR is enabled
EXECUTE sys.sp_configure
    @configname = 'clr enabled',
    @configvalue = 1;
RECONFIGURE;
GO
-- Lazy, but effective to allow EXTERNAL_ACCESS
ALTER DATABASE Sandpit
SET TRUSTWORTHY ON;
GO
-- The CLR assembly
CREATE ASSEMBLY FlowDistinctOrder
AUTHORIZATION dbo
FROM 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WITH PERMISSION_SET = EXTERNAL_ACCESS;
GO
-- The CLR TVF with order guarantee
CREATE FUNCTION dbo.FlowDistinctOrder 
(
    @ServerName nvarchar(128), 
    @DatabaseName nvarchar(128), 
    @MaxRows bigint
)
RETURNS TABLE 
(
    CustID integer NULL, 
    Amount float NULL
)
ORDER (Amount DESC)
AS EXTERNAL NAME FlowDistinctOrder.UserDefinedFunctions.FlowDistinctOrder;


Test table and sample data from the question:

-- Test table
CREATE TABLE dbo.Orders
(  
    OrderID    integer  NOT NULL IDENTITY(1,1),
    CustID     integer  NOT NULL,
    StoreID    integer  NOT NULL,
    Amount     float    NOT NULL
);
GO
-- Sample data
WITH  
    Cte0 AS (SELECT 1 AS C UNION ALL SELECT 1), --2 rows  
    Cte1 AS (SELECT 1 AS C FROM Cte0 AS A, Cte0 AS B),--4 rows  
    Cte2 AS (SELECT 1 AS C FROM Cte1 AS A ,Cte1 AS B),--16 rows 
    Cte3 AS (SELECT 1 AS C FROM Cte2 AS A ,Cte2 AS B),--256 rows 
    Cte4 AS (SELECT 1 AS C FROM Cte3 AS A ,Cte3 AS B),--65536 rows 
    Cte5 AS (SELECT 1 AS C FROM Cte4 AS A ,Cte2 AS B),--1048576 rows 
    FinalCte AS (SELECT  ROW_NUMBER() OVER (ORDER BY C) AS Number FROM   Cte5)
INSERT dbo.Orders 
    (CustID, StoreID, Amount)
SELECT 
    CustID  = Number / 10,
    StoreID = Number % 4,
    Amount  = 1000 * RAND(Number)
FROM FinalCte
WHERE 
    Number &lt;= 1000000;
GO
-- Index
CREATE CLUSTERED INDEX IX 
ON dbo.Orders 
    (StoreID ASC, Amount DESC, CustID ASC);


Function test:

-- Test the function
-- Run several times to ensure connection is cached
-- and CLR code fully compiled
DECLARE @Start datetime2 = SYSUTCDATETIME();

SELECT TOP (500) 
    FDO.CustID
FROM dbo.FlowDistinctOrder
(
    @@SERVERNAME,   -- For external connection
    DB_NAME(),      -- For external connection
    500             -- Number of rows to return
) AS FDO 
ORDER BY 
    FDO.Amount DESC;

SELECT DATEDIFF(MILLISECOND, @Start, SYSUTCDATETIME());


Execution plan (note the validation of the ORDER guarantee):



On my laptop, this typically executes in 80-100ms. This is nowhere near as fast as the T-SQL rewrite above, but it should show good performance stability in the face of different data distributions.

Source code:

using Microsoft.SqlServer.Server;
using System.Collections;
using System.Collections.Generic;
using System.Data.SqlClient;

public partial class UserDefinedFunctions
{
    private sealed class ReverseComparer&lt;T&gt; : IComparer&lt;T&gt;
    {
        private readonly IComparer&lt;T&gt; original;

        public ReverseComparer(IComparer&lt;T&gt; original)
        {
            this.original = original;
        }

        public int Compare(T left, T right)
        {
            return original.Compare(right, left);
        }
    }

    [SqlFunction
        (
        DataAccess = DataAccessKind.Read,
        SystemDataAccess = SystemDataAccessKind.None,
        FillRowMethodName = "FillRow",
        TableDefinition = "CustID integer NULL, Amount float NULL"
        )
    ]
    public static IEnumerable FlowDistinctOrder
        (
        [SqlFacet (MaxSize=128)]string ServerName, 
        [SqlFacet (MaxSize=128)]string DatabaseName,
        long MaxRows
        )
    {
        var list = new SortedDictionary&lt;double, int&gt;
            (new ReverseComparer&lt;double&gt;(Comparer&lt;double&gt;.Default));

        var csb = new SqlConnectionStringBuilder();
        csb.ConnectTimeout = 10;
        csb.DataSource = ServerName;
        csb.Enlist = false;
        csb.InitialCatalog = DatabaseName;
        csb.IntegratedSecurity = true;

        using (var conn = new SqlConnection(csb.ConnectionString))
        {
            conn.Open();
            using (var cmd = conn.CreateCommand())
            {
                cmd.CommandText =
                    @"
                    SELECT
                        O.CustID, 
                        O.Amount
                    FROM dbo.Orders AS O
                    WHERE 
                        O.StoreID = 1 
                    ORDER BY 
                        O.Amount DESC";

                int custid;
                double amount;

                using (var rdr = cmd.ExecuteReader())
                {
                    while (rdr.Read())
                    {
                        custid = rdr.GetInt32(0);
                        amount = rdr.GetDouble(1);

                        if (!list.ContainsKey(amount))
                        {
                            list.Add(amount, custid);
                            if (list.Count == MaxRows)
                            {
                                break;
                            }
                        }
                    }
                }
            }
        }
        return list;
    }

    public static void FillRow(object obj, out int CustID, out double Amount)
    {
        var v = (KeyValuePair&lt;double, int&gt;)obj;
        CustID = v.Value;
        Amount = v.Key;
    }
}