There was no database update when moving from 1.6 to 1.7, so I am sure the current database upgrade should work. Don't forget that you must run convdb tool
to update correct number of posts, topics etc. Don't pay attention that it suggests 1.7 version at least - it should go fine for any version if you have updated the database properly.
Also, you must add new options to setup_options.php (specially $dbUserSchema - it will affect the login issue) and restore each and every point described under Updates History
Of course if you did some custom changes, they will be lost. 1.6 is really an outdated version.