Generally speaking you can alter a site's design without having much effect on the functionality. However if you did alter any of the functionality you could potentially cause it to not work.
It would be best to evaluate the current state of the site and to also determine exactly how you would like it to be, then come up with a strategy based on that. The design stuff should not affect the sites functionality, but if you wanted to alter any of the existing functionality you would essentially be recreating it with the tools in Super Suite.
I would definitely suggest that before you start this you create a good backup of the current site, then when modifying it try to update just one thing at a time and do testing to determine if it working out.