Yes, you can use Elgg this way. You would have to set default access to public in admin panel, remove links to friend requests and remove or overwrite input/access view. This is a quite simple modification, but has to be done as a plugin. As far as I remember, you can't just choose settings for this behaviour.
The thing is it's not exactly public, poeple must have an account and loggin to get access to the information. The public (not logged) section of the site shoudn't display any information. I guess if I can set default access to public there must be a way to set it to logged right?
Use walled garden. Go to your Advanced site settings in the Admin panel and check Users must be logged in ...
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