Yes.
But if you would like to keep someone from knowing if you are online/offline, you can simply add that person to your Invisible List.
Follow these steps in order to do this:
- Click Menu > My tools > Settings.
- In the Settings window, click Privacy from the Advanced list on the left.
LI>Click Manage Block and Invisible Lists, and click the Invisible tab.
- Move the person you want to add to your Invisible list to the Always Invisible list.