Sql-server – A tail-log backup of the source database will be taken ? Why I am seeing this warning

Paul Randal did a good piece on backing up the tail of the log that includes just this case. In it he says that the method to use when there is no data file is using NO_TRUNCATE. Based on that your command should be:

BACKUP LOG [AdventureWorks2012] TO
DISK = N'C:\sqldata\MSSQL11.MSSQLSERVER\MSSQL\Backup\AdventureWorks2012.bak' 
WITH NAME = N'AW Tail Log Backup', NO_TRUNCATE

BOL does say

To perform a best-effort log backup that skips log truncation and then take the database into the RESTORING state atomically, use the NO_TRUNCATE and NORECOVERY options together.

So you could try using both of them together but I'm not sure if NORECOVERY can be used if the data file is missing or not, even with NO_RECOVERY.

BACKUP LOG [AdventureWorks2012] TO
DISK = N'C:\sqldata\MSSQL11.MSSQLSERVER\MSSQL\Backup\AdventureWorks2012.bak' 
WITH NAME = N'AW Tail Log Backup', NO_TRUNCATE, NORECOVERY

It's certainly worth testing anyway.

Normally when you want to restore a database from a different server, you're looking to create a device backup to a network drive, and restore from that.

The way the restore from database interface works is by querying the msdb database for recent backups, to see what you can restore. Accordingly you should be using a device backup:

If the backup is taken from a different server, the destination server will not have the backup history information for the specified database. In this case, select Device to manually specify the file or device to restore.

As the msdb database on server 2 will have no knowledge of the backups taken on server 1.