Is it possible to add an action to the currently running action?

You have to use a later (higher) priority. So use current_filter() to get the current hook and priority, add 1 to that priority, and register the next action:

add_action( 'init', 'func_1' );

function func_1()
{
    global $wp_filter;

    $hook = current_filter();
    add_action( $hook, 'func_2', key( $wp_filter[ $hook ] ) + 1 );
}

function func_2()
{
    echo 'hi!';
}