Yes, you should be able to install on a live site without any issues. Once you enable our system plugin, most of our functionality becomes active. However, if you don't enable the SCLogin module (or make it in an obvious place), the standard login functionality won't appear anywhere for someone to use. The same goes for a lot of other features.. you need to make them visible if you want to use them.
Of course, we'd always recommend installing on a dev site first and testing before going straight to a live/real site as you never know what can happen. We'll help with any issues you run into either way though.
Thanks,
Alex