Almost all of WhatsApp's 60 or so people were engineers at the time of the FB acquisition.
No. There is no way to build a billion dollar business without a management team. The founding team of a startup is a very significant part of the evaluation of any early-stage investor. Furthermore, regardless of the business of the app, there are critical business decisions and actions required of any business.
It doesn't mean that engineers can't fulfill the business roles and responsibilities (although at some point, this is likely the case), but it means that as a business grows, management responsibilities are required to run the company.