Can I set the mail settings in wp-config.php?

Yes. Define TRML_HOST, TRML_PORT, TRML_ENCRYPTION, TRML_USERNAME, TRML_PASSWORD, TRML_FROM_EMAIL, TRML_FROM_NAME or TRML_PROVIDER in wp-config.php and that value is used for the site, whatever the Settings screen says. The screen shows each of those fields greyed, saying Set in wp-config.php, and the password box stays empty: a password set there is never shown or stored. Saving the screen, or importing a settings file, does not change them. Take a constant out and the screen's own value is used again.

The test, the daily sign-in check and the commands all use them. On a network they apply to every site, and a must-use plugin can give one site its own through the trml_constant_values filter. The documentation has the whole list, with what each one takes.