Who would know the employee's work better, her manager or the promotion committee? This reminds me of an interview process that does not include checking references.

A system like you describe would seem to favour the employee who is adept at promoting her work. It also might disadvantage employees who are better performers than promoters. It would fail to detect employees who are poor or average performers but adept at covering that up.

Does the promotion committee consult with the manager?

A system like this suggests the company is concerned about favouritism and may not trust managers. It also suggests they may be willing to blindly trust self-promoting employees without knowing much about them.

How does the system account for high-performing employees that are too busy working to prepare presentations for promotion committees? Is there no such thing as an unsolicited promotion based on performance under this system?

Surely managers are reporting on the employees they manage. Assuming that includes any information on performance, then a system like this could allow the company to ignore the issue of rewarding high-performers with promotions, unless and until those employees came forward and presented to a promotion committee.

However a system like this does seem potentially beneficial for employees who feel they are undervalued by their manager.