System: Windows XP SP 2 Home Edition, IE 7, Avira security suite, CCleaner slim build. More than once I've observed CCleaner trying to phone out when I activated it. I usually leave it at my desktop, I uninstall it when I'm done. I use a customized installation, without checking for an update. Avira says it attempts to establish a TCP connection through Windows Explorer. That happens only if I have a working (wireless) internet connection. Maybe it's just Avira ? I'm not sure about the version, a mouse right-click just locked my computer so I'm not going to try that again.
I think when you first install it, CCleaner tries to phone home to verify that you are installing the latest version, if it's not I guess it'd inform you of a newer build. I just block the connection and let it install. Apart from that, I opt not to automatically check for updates and I've never been alerted to any attempt made by CCleaner to access the internet.