Should 3rd Parties Use $wp_scripts/$wp_styles->add_data?

This function adds data to scripts/styles that have been enqueued during the WordPress load.

Not really. It adds data to scripts/styles that’ve been registered.

The data key that is set by wp_localize_script is ultimately overwritten by the call to $wp_scripts->add_data, whereas if you call wp_localize_script twice for the same script, the string will be properly concatenated.

Right. They both call the underlying (non-accessible, internal) API, so it gets overwritten (as you stated). This happens when it calls $this->get_data( $handle, 'data' );.

Question

My main question is: should developers be using this function?

Answer

Simply said: Yes, when you got no other chance to do what you need.

Another example: Check if a script was registered (for e.g. json2/jquery) and move it to the footer (check extra['group']).

// Move scripts to the footer - in case it isn't already there
if ( ! $wp_scripts->get_data( 'json2', 'group' ) )
    $wp_scripts->add_data( 'json2', 'group', 1 );

if ( ! $wp_scripts->get_data( 'jquery', 'group' ) )
    $wp_scripts->add_data( 'jquery', 'group', 1 );

Note: This ↑ only works for data filed under extra!

Additional notes

Counter-Question: Have you ever tried to add dependencies to scripts registered by core? For e.g.: Try to add JSON2 as needed deps to jQuery. This isn’t possible without intercepting the global $wp_scripts:

global $wp_scripts;

$scripts = array( 
     'jquery'      => array( 'json2' )
    ,'jquery-form' => array( 'json2' ) 
);

foreach ( $scripts as $handle => $deps )
{
    // Ugly hack: Intercept the global to force the "natural"/needed order: JSON2 » jQuery
    $deps_default =& $wp_scripts->registered[ $handle ]->deps;
    $wp_scripts->registered[ $handle ]->deps = array_merge( $deps_default, $deps );
}

There’s a whole load of things the class can’t do. So using something like ->add_data() is imo fully valid. Just use what you got, as it’s still better then living the lacks of core classes.