Hmm. Interesting question.
Unfortunately, you can't stop the program from accessing the net without modifying its source code and voiding parts which refer to tcpip requests.
What I would suggest is simply setting up your firewall to block access to all the IP addresses amaroK attempts to connect to.
Find out what these are by using any network activity monitoring tool and then adding clauses to your HOSTS file ( search for hosts.config as super user ) preventing any connection to the given location.
If you don't like manual editing of .conf files, a program called 'guarddog' will do it for you.
and do a search for your distro.
Now, the clear drawback here is that you won't be able to access any HOSTS blocked site from any web browser by doing this, for example amazon will be blocked (Where do the covers from amaroK's cover manager come from? Correct!), so I hope you're not an Amazon customer.
To be honest though, I can't really understand why you'd want to stop amaroK from accessing the net. It's not as if it's Windows Media Player and its sending all your private data to Micro$oft; its a good, honest GPL'd app that has absolutely no interest in what you do or don't listen to.
After all, why go penguin if we can't trust opensource?