Right now it's possible (though I suppose not advised) to attach a customer profile reference field with the manager widget to the user profile. However, the widget on its own never assigns a uid to a customer profile, because it's not able to assume the person creating a profile should be the owner of the profile. This is the primary use case of administrators creating customer profiles on order forms.

The order module implements an extra bit of logic to associate saved customer profiles to orders when those orders get uid properties. We can probably add a similar feature directly to the Customer module that assigns a uid to customer profiles created through user forms, but it must also be tested to ensure it gets it right on user registration forms.