The latest MAS version of Growl does support a history feature as well as rollup. The actual log files can be access from the history tab in Growl. Haven't tried copying to the clipboard but is possibly the closest you will get to this functionality.
I also found this article explaining how to enable a Growl log file to display using GeekTool:
touch ~/Library/Logs/Growl.log
defaults write com.Growl.GrowlHelperApp GrowlLoggingEnabled -bool YES
defaults write com.Growl.GrowlHelperApp GrowlLogType 1
defaults write com.Growl.GrowlHelperApp "Custom log history 1" /Users/kent/Library/Logs/Growl.log