Do my customers care whether my company is registered?
A company (or close corporation, for that matter) is only in existence if it is registered at the Companies and Intellectual Property Commission (CIPC), thus it would be very important for the customer otherwise the contracts concluded would not be of any effect.
However, as to whether you use a company or a sole proprietorship in the first place, it is debatable what importance a third party attaches to the legal form or entity that you use for your business.