Yes it is possible with PHP and MySQL.

I'm not aware of any plugins and it is not a trivial thing to program that I could just tell you how to do.

[DELETED]

I know a really good programmer that might be able to handle this for you if you are interested in outsourcing.

PM me if you want his info.

Leadz, some crazy suggestions so far. I'll try to give you some direction.

If you want to custom code this, you can go about it this way:

1. Hook into the user_register hook.
Plugin API/Action Reference/user register « WordPress Codex

2. Use the wp_insert_post function to add a post for the new user:
Function Reference/wp insert post « WordPress Codex

You'll want to lock down the page so others can't stumble upon it. So you can:
3. Add post meta (call it "my_user_id" or something) with the user_id of the user the page was created for:
Function Reference/update user meta « WordPress Codex

4. Create a page template that checks that post meta against the current user. Something like this at the top of the template:
---
global $post, $current_user;
$page_user = get_post_meta($post->ID, "my_user_id", true);
if($page_user != $current_user->ID)
{
wp_redirect(home_url()); //redirect them home
exit;
}
---

When you create the page after the user registers, you'll have to set the template. Here's a note from the wp_insert_post Codex page:
NOTE: The page_template key was removed from the $post table and is now located in the wp_postmeta table. To set the page template of a page, use update_post_meta instead with a meta key of _wp_page_template.

Hope this helps.

Are you stuck on Wordpress? It sounds to me like you're wanting more of a support desk where the user opens a ticket for work and only that user can see the ticket. You update the ticket in progression until it is closed either by you or the user. Is that like what you want? I could use Drupal for something like that or perhaps another Open Source framework. I'm not too familiar with Wordpress these days but tend to think of it more of a blog tool.