By this trick you can easily know if a person is invisible or not.
just follow these steps:
Login using G-talk. (not in gmail or orkut)
Find the person in the list whom you want to check if invisible.
Open the chat box and select 'Go off the record' option from the popup list.
After that type some message and send it to him.
If the message shown in yellow box here is displayed, then he is presently offline. Otherwise you will get a message telling about your 'off record' situation.