Hi Frank,
I know that in the Roster Admin settings for events, you can restrict visibility to only registered players (in that league). That way, if someone clicks on the Google link to the roster, they'd only be able to see that so-and-so is on it, if they're logged into a player account that was registered in that event. Of course, Google has probably cached the roster, but c'est la vie, non?
I do not know of a way to restrict visibility of a player page that lists all registered events & teams, but the only personal info displayed is name (which is what's being searched upon, so not a give-away in the proposed scenario).
Hope that helps!
- Josh @ TFDA