Ajax Register for Multiple Apps

I'm looking for a solution to allow users to register only once, with one user name, and access different front end areas of the site.

Storefront
Forum
Registration (such as DT register)
etc.

Will Ajax register handle this, and is it simply a matter of Joomla configuration, or will I need additional extensions to make this work?

You need additional extension and bridges for that. AJAX Register merely offers a more convenient way to register.