Thanks Chip (excellent Settings API tutorial) and t31os (great snippet of code for quick testing) for both your suggestions.
I did some further digging and found that the default messages can indeed be displayed if I hook into any menu but only if the function settings_errors() is called.
For example, modifying t31os code as follows:
<div class="wrap">
<h2>Test</h2>
<?php settings_errors(); ?>
<form action="options.php" method="post">
Custom error messages can also be added by calling the add_settings_error() function for displaying success or failure message by specifying the $type
parameter as either ‘error’ or ‘updated’.