It really depends on the role that you are applying into.
For entry level, no professional managerial experiences are required. However, "leadership experiences" in various settings from academic to extracurricular activities are essential to be displayed. For example, leading a group of researchers in you university on a novel research project or a team of students in a business case competition.
For experienced hires at manager level and above (or even associate / senior associate level in some cases, depending on how large is the organization where you have your managerial experience compared to the target consulting firm), it is typically required for prospective candidates to have managerial experiences. I have to say that for some firms (e.g. MBB), to be directly appointed into a manager role, one typically needs to have a significantly more senior role at the previous companies (e.g. senior manager, head, chief, etc - again this varies depending on the size of your previous company).
There will always be exceptions, for example, someone coming from unique background such as musicians or performers. They might have experiences in leading a symphony or performing troupe, which will be evaluated as leadership experiences. Others might have a very high proficiency on specific knowledge domain, hence displaying a strong knowledge leadership.
Leaderships can be displayed in multiple ways from management, knowledge development, client cultivation, and so on.
It is good to remember that the 2 most important elements that the firms would like to see on their prospective candidates are:
- Problem-solving skills
- Leadership traits (including accompanying behaviors such as internally driven, tenacity, etc)
Hope it helps.