EDIT

After some testing, I can see the dirty pages are not lost, but I am not sure why:

using this tutorial

create a test database

CREATE DATABASE DirtyPagesDB
GO
USE DirtyPagesDB
GO

turn off automatic checkpoints

DBCC TRACEON(3505, -1);
DBCC TRACESTATUS();

create a table, insert some data and issue a checkpoint:

CREATE TABLE t1 (Speaker_Bio CHAR(8000))
GO
INSERT INTO t1 VALUES ('SQL'),('Authority')
GO
CHECKPOINT

confirm no dirty pages

-- Get the rows of dirtied pages
SELECT
database_name = d.name,
OBJECT_NAME =
CASE au.TYPE
WHEN 1 THEN o1.name
WHEN 2 THEN o2.name
WHEN 3 THEN o1.name
END,
OBJECT_ID =
CASE au.TYPE
WHEN 1 THEN p1.OBJECT_ID
WHEN 2 THEN p2.OBJECT_ID
WHEN 3 THEN p1.OBJECT_ID
END,
index_id =
CASE au.TYPE
WHEN 1 THEN p1.index_id
WHEN 2 THEN p2.index_id
WHEN 3 THEN p1.index_id
END,
bd.FILE_ID,
bd.page_id,
bd.page_type,
bd.page_level
FROM sys.dm_os_buffer_descriptors bd
INNER JOIN sys.databases d
ON bd.database_id = d.database_id
INNER JOIN sys.allocation_units au
ON bd.allocation_unit_id = au.allocation_unit_id
LEFT JOIN sys.partitions p1
ON au.container_id = p1.hobt_id
LEFT JOIN sys.partitions p2
ON au.container_id = p2.partition_id
LEFT JOIN sys.objects o1
ON p1.OBJECT_ID = o1.OBJECT_ID
LEFT JOIN sys.objects o2
ON p2.OBJECT_ID = o2.OBJECT_ID
WHERE is_modified = 1
AND d.name = 'DirtyPagesDB'
AND
(
o1.name = 't1'
OR o2.name = 't1'
);
GO

confirm time of last checkpoint

SELECT  f1.[Checkpoint Begin], f2.[Checkpoint End]
FROM    fn_dblog(NULL, NULL) f1
        JOIN fn_dblog(NULL, NULL) f2
             On f1.[Current LSN] = f2.[Previous LSN]
WHERE   f2.Operation IN (N'LOP_BEGIN_CKPT', N'LOP_END_CKPT');

Add more rows

INSERT INTO t1 VALUES ('SQL'),('Authority')

Use query above to confirm that there were dirty pages

Kill the SQL Server task from task manager to simulate a power off.

Start the service

Re-run the command above to get the last checkpoint time, it was the same (IE no checkpoints have run other than the one we did manually)

SELECTed from the table t1 and all four records were there