I don't think, so the system takes the default one.
This can help you :
This is a part of my function.php file
/*
#######################################
Déclaration des sidebars et boites de Widgets WordPress
#######################################
*/
// Sidebar #1 par défaut
if ( function_exists('register_sidebar') )
register_sidebar();
// Sidebar #2 (single.php)
if ( function_exists('register_sidebar') )
register_sidebar(array(
'name' => 'Sidebar2 - single.php',
'before_widget' => '<div id="sidebar"><ul><li>',
'after_widget' => '</li></ul></div>',
'before_title' => '<h2>',
'after_title' => '</h2>',
));
// Sidebar #3 (category.php et tag.php)
if ( function_exists('register_sidebar') )
register_sidebar(array(
'name' => 'Sidebar3 - category.php et tag.php',
'before_widget' => '<div id="sidebar"><ul><li>',
'after_widget' => '</li></ul></div>',
'before_title' => '<h2>',
'after_title' => '</h2>',
));