Yes, if you do not use the default wiki as homepage.
Try it step by step:
1) Remove all 'Anonymous' group permissions
2) Grant wiki read permission wiki to group 'Registered'
3) Run a test
4) Change homepage (this is the complex part, example for a blog)
4a) activate feature blog
4b) create a blog
4c) set it as default blog
4d) change Tiki homepage to blog
5) Re-adjust permissions
This is the basic idea, maybe some finetuning steps are missing. If (when) everything works:
6) Write a little howto documentation for our doc.tiki.org website or post a step-by-step howto here (forum).
7) Enjoy and have fun