Does WordPress theme customisation API support section hierarchy?

Yes, this is supported. They’re called panels, sections and controls.

Adding a panel uses this code:

$wp_customize->add_panel( $panel_name, array(
   'title'                      => 'panel_title',
   'description'                => 'panel_description',
   'priority'                   => 'priority',
   'capability'                 => 'edit_theme_options',
   'theme_supports'             => ''
    ));

Adding a section goes like this:

$wp_customize->add_section($section_name , array(
    'panel'                     =>  'panel_name',
    'title'                     =>  'section_title',
    'description'               =>  'section_description',
    'priority'                  =>  'priority',
    'capability'                =>  'edit_theme_options',
    ));

Adding the controls is a bit more complicated, but well described in the codex.