Your milage may vary. A project can succeed without a project manager, but running a project without controls is a business risk that must be accepted by the leadership team.
A project doesn't need a project manager unless the project needs to be managed! However, every process needs a process owner. In a formal project, the process owner for a project is usually the project sponsor, although responsibility for managing the project is usually delegated to a project manager.
Whether or not your organization needs an actual project manager for this specific initiative is entirely up to your leadership team. Starting a project without a project manager or any formal project controls is simply a business risk; it's up to your company executives to measure that risk, and then determine if the level of risk is acceptable or not.
A better question is: What happens if you later determine that the project does need a project manager? If your leadership team is unlikely to give the project the necessary time to stop the line, inspect the process, and adapt it where needed in the event that the initial laissez faire approach doesn't work, then you're better of starting out with a more formal framework than trying to retrofit one later.