A think it depends on what you mean by "management task." If you take the initiative to drive a really valuable project, can assume a leadership role while ignoring a lot of the tasks the company typically assigns to a manager, like performance reviews and meetings and ticket/bug metrics and timesheets and project plans and timelines and deadlines and fielding every request that comes your group's way.

Meanwhile a good leader will drive and inspire the team by making and pushing excellent design decisions, obtaining needed resources, doing the oxen's share of grunt work to get the project off the ground, and energetic mentoring of other developers.