The Internet access feature is neither a replacement for a proper firewall, nor was it designed as a mechanism to counter or hinder key-loggers.
Some key-loggers could possibly circumvent the Internet access restriction by hijacking the Web browser to be used as a vehicle through which to send out the recorded information.
That should work - except for webpage script loggers.
In the case of webpage script loggers the only thing that can potentially block logging is a encryption - like HitmanPro.Alert, SpyShelter or KeyScrambler.
However, I think the likelihood that they will protect against webpage script logging is low.
Something like NoScript or equivalent might do a better job of it.