I don’t believe so…I’m following this as I’m looking to make some changes to the register-form.php file as well.
Don’t quote me on this, but I think Jeff is saying that you will have to enter new registration_errors and new tml_new_user_registered variables to the theme-my-login-custom.php file for each additional item you wish to add to your register-form.php file. Jeff’s example only shows how to add a line for Companies (user_company, empty_company).