I'm a hobbyist roboticist, and robotics is a wide field, requiring many disciplines. I suspect the general answer for what you'll do in the workplace is that it depends on the size of the company you work for. In a smaller company, you'll be able to wear more hats. In a large company, you'll be more specialized. In any case, it is always valuable to understand the big picture -- if I hire you to build a better bot, and you know how to code but understand what happens with the electronics, you are definitely more valuable to me than someone who merely knows how to code; the same is true if you are an electrical or mechanical engineer and understand how what you are doing relates to the other disciplines in the project.
I was previously a game programmer. The question is akin to asking, "I want to make video games for a living. Can I be a game engineer and a programmer?" For a very small company (say, less than three people), you can do it all -- make art, design the game, and do the programming. As most people can not do all those things well, in a mid-sized company, you'll either be an artist, a designer, or a programmer (or possibly a liaison of sorts, such as a technical artist). On an even larger team, the answer to "I want to program games" becomes "Do you want to do the front end? database? animation? artificial intelligence? rendering?" with each being its own special subfield.