Can you use dynamic custom questions?

[MashMashy]

This is long, but important, at leat to us. Thank you in advance for reading.

Here's the one thing holding us back from buying vBulletin (can't find a definite answer on
this), and why we are using phpBB - the possible inability to use a customized hash input on registration to restrict usernames.

Let me explain exactly what we are doing on our current board for our company, so you know where I'm coming from.

To register on our company's current board (4700-ish users), your login name must be equal to your corporate account email prefix (bobmjones123@nameofcompany.net must use bobmjones as their login name).

To facilitate this, when bobmjones logs into their corporate workstation (not forum), they have the option of 'getting the forum hash' for their account name. Then, when registering on our forum, they enter the username 'bobmjones', and their custom question's answer (think like an anti-spam question) is their hash number, which is derived mathematically from their username. The phpbb backend calculates what their hash should be based on their username (in the PHP code), and if it doesn't mach the inputted hash, it denies their registration.

Important point, to reiterate:
The hash isn't something like "accept the answer 'Yes', 'yes', or 'YES'". The variable compared to their inputted hash is calculated mathematically using their inputted username as a seed. think of it as a much more complicated "if the number they entered for their custom answer is the exact sum of all of the ascii cahracters in their chosen username, allow the registration".

Is this something - even with custom coding - that can be done with vBulletin?

Even something like "you can close registration, but use this standalone PHP module X to externally create users on the forum" would be satisfactory - they could 'click this link to auto-create their forum login, and then login and change their password'. Anything that will allow us to automatically create logins, or dynamically verify logins, would be sufficent.

If so, I'm authorized to buy a life membership for the company ASAP. However, nothing I can find, anywhere, can answer this question satisfactorily.

Thank you so much for any help you can be.