Transaction Replication Without Snapshot
What version of SQL Server are you using ?

I just setup a publication and subscription in the method you describe on SQL Server 2012 (11.0.2218) and it appears to be working fine.

I tested inserting, updating, and deleting records from the source - and all transactions made it successfully to the destination.

It is true that the timestamp column is of interest but I didn't have to use the option you mentioned in your update.  From this SQL 2000 TechNet article note that 


  "The literal values for a timestamp column are replicated, but the data type for the replicated values is changed to binary (8) on the Subscriber."  


Since this was for SQL 2000 I can only imagine things may have changed... as my subscriber table, just like the publication, has a timestamp column not a binary(8).

Therefore the values that are there when you backup and restore will match.  Future inserts will have different timestamp values in the source and destination.

I scripted the entire thing out into one file.  The order of events: 


create the publication (with @allow_initialize_from_backup = N'true'); 
backup the source database (with format, init); 
restore the database to the destination; 
create the subscription (with @sync_type = N'initialize with backup', @backupdevicetype = 'disk', @backupdevicename = '\myUNCPath\Backup\Backup.bak').


I ran into Msg 21397 during my first try - and an interesting read, explanation, solution are in this blog post.