Bulk insert generated ids return order

Question

I want to very efficiently execute a bulk insert of a DataTable to SQLServer from a C# application and retrieve the inserted ids in the right order. In order to get the inserted primary keys auto incremented values I use the following approach on the same connection:

1. create table #StagingTable(....) "
2. BulkInsert DataTable into #StagingTable

3. execute a reader on:

   insert into DestinationTable(....<columns_list>...)
   output inserted.ID -- primary key which is auto increment
   select <columns_list> from #StagingTable
   

4. then in C# I read all the generated ids in a list. The read order is not correctly mapped to DataTable.Rows order.

My question is: If I sort this list of ids ascendingly without doing any mappings (i.e. c# simple: list.Sort()) - will this be the correct inserted order so that table.Rows[k] corresponds to id = list[k] ?

Thank you!

/Edit:

To give you the full context, I have a method like this in C#

using System.Data;
using System.Data.SqlClient;
using System.Web.UI.WebControls;

public static class SQLWrite
{
    public static void BulkWrite(this DataTable table, string destinationTable, SqlConnection connection, int batchSize)
    {
        if (connection.State != ConnectionState.Open)
        {
            connection.Open();
        }
        string columnNamesAndSQLType = string.Join(", ", Enumerable.Range(0, table.Columns.Count).
            Where(i => !table.Columns[i].AutoIncrement).
            Select(i => "[" + table.Columns[i].ColumnName + "] " +
                Parameter.ConvertTypeCodeToDbType(Type.GetTypeCode(table.Columns[i].DataType)).ToString()));
        string columnNames = string.Join(", ", Enumerable.Range(0, table.Columns.Count).
            Where(i => !table.Columns[i].AutoIncrement).
            Select(i => "[" + table.Columns[i].ColumnName + "]"));
        using (var command = connection.CreateCommand())
        {
            command.CommandText = @"
CREATE  TABLE #StagingTable(
    RowNumber INT IDENTITY(1, 1) NOT NULL, 
    " + columnNamesAndSQLType + @")     ";
            command.ExecuteNonQuery();
        }
        DataColumn autoIncrementColumn = null;
        using (var copy = new SqlBulkCopy(connection))
        {
            copy.BatchSize = batchSize;
            copy.DestinationTableName = destinationTable;
            foreach (DataColumn column in table.Columns)
            {
                if (column.AutoIncrement)
                {
                    autoIncrementColumn = column;
                    continue;
                }
                copy.ColumnMappings.Add(new SqlBulkCopyColumnMapping(column.ColumnName, column.ColumnName));
            }
            copy.WriteToServer(table);
        }
        using (var command = connection.CreateCommand())
        {
            command.CommandText = @"
INSERT  INTO dbo.DestinationTable(" + columnNames + @")
OUTPUT  INSERTED.ID 
SELECT  " + columnNames + @"
FROM    #StagingTable 
ORDER   BY RowNumber    
";   //Will the inserted ID values be retrieved in the natural order of insertion - by RowNumber ?
            using (var reader = command.ExecuteReader())
            {
                List<long> list = new List<long>();
                while (reader.Read())
                {
                    list.Add(reader.GetInt64(0));
                }
                list.Sort();
                int rowIndex = 0;
                foreach (DataRow row in table.Rows)
                {
                    row[autoIncrementColumn] = list[rowIndex];
                    rowIndex++;
                }
            }
        }
        if (connection.State != ConnectionState.Closed)
        {
            connection.Close();
        }
    }
}

Assume each table has a bigint primary key auto-increment column called ID. I want to know if the above code retrieves the SQL generated IDS and associates them with the data table correctly.