Yes
.
I'm not saying you need to do people management, but anyways, you need to be able to
- Lead a team and be part of one
- Understand the challenges and provide help to solve them
Now, you can either be in a very technical-oriented role, or a solely people-management role, either way you need to do these. Based on your role, the activities will change, but no matter what you need to be able to collaborate, lead and manage.
So if you don't want to manage people, is it possible to succeed/get promoted?
Well, if you're having a technical role, it's generally not needed to manage people (ex: managing timesheet. leave, performance appraisal etc.), but unless you can handle a team (ex: roadmap, architecture, problem solving, learning), it's not possible to succeed. Note: promotion != success.