Can I have buddies in iChat that are not in Address Book?

Yes.

If you create an AIM buddy in iChat, an entry for that buddy is automatically added to your address book. You can then erase that entry in your address book, and your buddy will remain in your AIM contact list. Ta-da.

Another entry for my book, The Mysterious Idiocies of iChat.

Of course you don’t have to erase the entries from your address book however if you have an iPhone and sync your contacts you may want to delete all the entries in the the address book that are just screennames.

My ichat contacts don’t show up in adress book.

@wilhel1812 Are they AIM contacts?

Yes.

@wilhel1812 Hmmm that’s odd maybe I have mine setup to automatically add my AIM contacts to my address book.