The registration processing is not a part of Simple:Press but is all handled and controlled by WordPress.
The best way to achieve what you are asking for would probably be some sort of simple membership plugin where you can control what WordPress ‘role’ users are placed in. If the plugin sticks to WP standards AND the WP API (as it should) then when the WP ‘role’ is allocated – this can be mapped to a Simple:Press user group. This is, in effect, what we do on this site to differentiate gold and silver members and setting it up is much easier than it sounds.
There is, in fact, a ‘How To FAQ’ on out codex covering this although that uses WishList Member for the membership plugin. There are quite a few others and probably simpler ones I believe.