Can a majority shareholder appoint themselves as CEO?

There's being the majority holder, and there's being a person with a control of the majority of the stock, either outright or by proxy.

A majority holder may be someone who has 5% or more of a stock. In today's business world, a major player, but not necessarily one with a controlling interest.

On the other hand, the person may own 51%, or be able to vote 51% through alliances and proxies. If so, they could probably appoint themselves CEO, but usually not outright.

It would be a matter of asking the Board. There are rules and procedures to follow. Of course, given control of 51%, these would be a formality. If it came to it, there'd be dismissals and appointments of various board directors until the vote went the proper way.

Also, a person wouldn't necessarily have to have 51% control to be appointed CEO. What is primarily needed is to show that you have the savvy to make the company money. That and that you are focused on it - usually by having that 5% personally owned.