Other options would be
function_exists( 'first_loaded_plugin_fn' ) AND do_something();
class_exists( 'initial_plugin_class' ) AND do_something();
The best chance is the callback function from register_activation_hook( $file, $function );
if the plugin does not only offer a template tag or similar basic functionality.
or:
Some option from the plugin that get's added on init/activation:
echo ! empty( get_option( 'plugin_option_name' ) ) ? 'activated' : 'not active';
or:
Check if the plugins_loaded hook has some action (<-- link)
echo has_action( 'plugins_loaded', 'fn_to_check') !== false ? 'activated' : 'not active';
You'll hacve to take a closer look at the returned result. The result may contain the priority too.