Can I pass parameters to the add_shortcode() function?

You can use a closure for that together with the use keyword. Simple example:

$dynamic_value = 4;

add_shortcode( 'shortcodename', 
    function( $attributes, $content, $shortcode_name ) use $dynamic_value 
    {
        return $dynamic_value;
    }
);

See also Passing a parameter to filter and action functions.