The Six Sigma management method philosophy focuses on better understanding of customer requirements, improving business systems throughout the organization, and enhancing the organization’s financial performance. It is used to improve the organization’s products, services and processes across various disciplines, including production, product development, marketing, sales, finance, and administration.
With the definition given its seems likely to apply six sigma for project management but it looks like it come with a lot of risk.
Let me show here what I mean by dividing project management into various topics

Scope: When we apply six sigma principal to scope it make your scope to definitive of requirements and rigorous change management. The risk here would be no innovative idea.

Scheduling: If six sigma principal are used in Scheduling you schedule is no longer flexible all deadline are rock fixed as there is no room to adjust. This puts pressure to have that extra padding or buffer while scheduling.
Cost: Applying Six Sigma in cost management would imply absolute budgets, enforce careful cost controls, and effective forecasting. The risk may be that this application could encourage additional budget padding and increase reserves.
Quality: Applying Six Sigma in scope management would enforce unyielding quality targets, careful selection of standards, and realistic assessment of capabilities. The risk may be that this application could result in hiding problems and assigning blame for defects to others.

With all the risk and benefits taken into account I think applying six sigma on Project management definetly has its perks but it would highly depend on type of product . In case of Medical device six sigma would be very tough or next to impossible to apply because of the uncertainty from regulatory and other departments.