Keeping database in synch
No.  In order for a log to be restored to a database, the log sequence number (LSN) of the log has to be the correct number to match what the database requires for the next log to be restored.  If you could somehow get the LSNs to match, restoring a log from a different database would corrupt it as some operations contain page IDs, and the page IDs are not going to be the same on both databases.

There are probably quite a lot of other reasons why this won't work, but it really isn't necessary to document all the reasons why as it is something that is simply not designed or expected to be able to work that way.