Does this function wp_get_nav_menu_object check if a nav menu exists or is supported?

The answer is in the source code that you posted.

The code attempts to get the menu by ID using get_term, then by slug and name using get_term_by. If nothing is found it returns false, here:

if ( ! $menu_obj )
    $menu_obj = false;

Hata!: SQLSTATE[HY000] [1045] Access denied for user 'divattrend_liink'@'localhost' (using password: YES)