Yes, that's how it works for larger cooperatives where direct democracy can become problematic. Even in direct democracies in societal level, presidents are typically elected, and there are ministers and managers by necessity. The same goes for cooperatives.
It's one person one vote applied to the corporation. In principle there's no reason why we should demand any less democracy inside corporations than what we demand in societies at large.
It's curious how many of these comments in this post could be reframed to be basically: "democracy can never work" or "democracy is clearly an inferior system to feudalism".
