You don't need Admin access to install Postaci on your account, unless you're on an NT server.
Since Postaci lacks a registration form, it will use vBulletin's to register new users, and NO, you don't need to register users 1
by 1 in the Control Panel.
You can try installing another PHP email client, PHP POP3, in your account to see how everything works.
http://ractive.ch/popper/index.php
The only problem with Postaci is that it requires IMAP functions compiled into PHP. It's a simple, little module that your host might not offer. But it never hurts to ask.
Here's a little feature I plan to add that can be very useful. After sign up, and instead of the regular vBulletin Welcome Page, users will have 3 links to choose from: Classifieds, Email, or Forum.