Eric,
When you click the Register button in the SCLogin module, you're redirected to the Joomla registration page. That page is completely controlled by Joomla and the SCLogin module doesn't function or interfere with that process.
Doing a little research, it actually seems that Joomla 3.2.0 changed the username behavior and no longer allows usernames with spaces in them. The same was also implemented in Joomla 2.5.15. However, due to backward compatibility concerns, the change was reverted in both Joomla 2.5.17 and Joomla 3.2.1. You can see the release notes for 3.2.1:
developer.joomla.org/version-3-2-1-release-notes.html
Specifically, if you search for 'username', you'll come up with the tracker issue below:
joomlacode.org/gf/project/joomla/tracker...racker_item_id=32883
I also just tested on a Joomla 3.2.1 site and was able to register a username that used a space.
I know you mentioned that you're using Joomla 3.2.1 above, but I'd highly recommend ensuring that you fully upgraded your site and that everything upgraded as it should.
I hope that helps explain, but should you need anything else, just let me know.
Thanks,
Alex