Is this a standard block or a third-party block? I would tend to think making a change to the block itself would be better, rather than making a change to Moodle core.
You might look at how I did this in the Course Creation block - basically, I do a check to see what access the user has and display the appropriate content. Nothing displays at all if they are not logged in. If you didn't want to do a check for their level of access, you could wrap your block with if isloggedin()
Thanks,
Matt