Comments will remain screened only if you put something along the lines of "Privacy, please!" in the subject line. (Likewise, their answers will also be screened*.) Otherwise, all comments and their threads will be unscreened, whether they are anonymous or not.
We look forward to hearing from you!
* Screened comments aren't viewable in lj inbox, so you should make sure you have emailing of comments turned on if you want private correspondence that you can actually read. :-)