Simple answer yes there are roles in almost every company you can think of. Its hard to get into some and they are pretty tiny. I am in a GM/Operation track for a manufacturing company, they hired another guy but he seems destined to be in their sales leadership and has no interest in operations. I am the only person in my path this year and they last hired people into it like 5 years ago (the last group are now regional managers overseaing several plants and GMs). They probably will hire 1-3 this year but it depends on the candidates.
Programs vary a lot and so does the expectations of where you will end up. Lots of companies will peg you as a project manager and nothing too high. Others will expect you to advance to run the company. I tend to think its better to be one of a handful of people in a large company. If you are the 1 of 1 to 3 people in a 10k+ person multi billion dollar company you probably are going to get a lot more opportuniities than someone who is 1 of 30 at a similar sized company.
There are a lot of odd companies that hire MBA's...everything from high tech to CPG to commodity companies. Some are easier to get in front of since they actively recruit a lot more and hire a lot of people. But you could find a direct competitor in the same industry with the same market share who doesnt hire much and may end up offering a better fit. Personally after doing and internship and lots of recruiting/networking I came to realize that function and the work you will be doing is personally more important than the industry or company. I want a true GM role and in the end that meant I needed a company that owned manufacturing plants and want me to eventually advance to running one. I found that plants are typically run as almost independent companies thus giving you the best chance to play mini CEO and run your own show.