Can someone who starts out as a Mechanical Engineer advance to become a CEO and would they still be able to practice engineering?

I would say that it probably depends on how big you want your company to be. It will be much more possible at a small company where everyone is more likely to be doing multiple jobs and wearing many hats. At larger companies as noted above, there tends to be too much other responsibilities to do actual engineering work,

There is never anything stopping you from engineering on your own time though, I have always known engineers to be looking for problems to solve everywhere, so you may find your engineering fulfillment in other areas while performing CEO duties. Additionally bringing an engineering mentality to a CEO position can be a great thing, you may not be engineering products, but problem solving and working on larger vendor or manufacturer issues could scratch that itch as well. Good luck with your career plan, it sounds like you certainly have a lot of drive and ambition.

Sincerely,
Blake Jenssen

Yes! You can start as an engineer and work your way up to become a CEO. Mary Barra is an electrical engineer and she is leading the biggest american car company at the moment. However, you won't be doing much engineering at that point. You would be too busy running a the business :)

https://en.wikipedia.org/wiki/Mary_Barra

In short yes. You can even start your career as a CEO and practice mechanical engineering. A lot of companies have started with people straight out of school. You have several great answers that explain this from different perspectives. At large companies, the CEO is rarely that hands on, but still uses his or her education and experience to make decision about the companies direction. The smaller the company, the more likely the person at the top is very hands on.