// Create a URL object
$url = \IPS\Http\Url::external( $API_URL );

// Now fetch it
try
{
	$response = $url->request()->get();
} catch( \IPS\Http\Request\Exception $e ) {
	return FALSE;
} catch( \RuntimeException $e ) {
	return FALSE;
}

if ($response->httpResponseCode == 200) {
	return TRUE;
} else {
	return FALSE:
}

Is this the correct way to validate that a url request is successful?

Yes, assuming that you consider a response code other than 200 to be unsuccessful (many APIs, for instance, may return response codes other than 200 validly).