Support for formal KM should be top down as there will be the need for an eventual spread of knowledge workers across the organization, not just within the PMO. Ideally, there is a separate KM group which will drive processes and practices. A Community of Practice will begin to create a collective of 'advocates' across the organization's departments.
That said, you could certainly spearhead a KM initiative. It has to start somewhere. With a solid plan and strategy, the PMO can help drive the importance of KM practices, exposing the value to the organization through results.
The role of Knowledge Management and Innovation management is subjective to the reason for which the PMO is established. You must be aware that a PMO is developed based on the needs of the organization and the value it seeks to add.
I'm of the view that no matter what the purpose of the PMO is, it does eventually comes down to knowledge management and innovation management.
If you seek to establish its awareness and maturity, I would suggest to take it as COMMUNITY work among the teams/across the organization. The PMO will lead the way. Saving Changes...
I belongs to a "special" PMO division inside my actual workplace: Innovation and Transformation EPMO (Enteprise PMO). My responsability is leading critical success factor programs in Latin America as a whole. This division was created because the whole organization was transformed implementing Agile in order to gain into agility (take into account that Agile is not software related, is not a method, is not a process. Agile was born as enterprise wide discipline inside USA DoD NSF/Agility Forum in 1990 where I was part). So, you are asking for two items. First of all, Knowledge Management, it is critical to lot of things but mainly to implement Agile. There is no way to implement Agile and gaining in agility without Knowled Management by definition of Agile. We create a whole Knowledge Management system (system is not used as synonim of software system) whichi demands to take into account a whole architecture mainly based on what today some people named "Big Data" but is a Data Wareshousing architecture. Knowledge Management got to us the basement for Innovation. As you know Innovation is a new buzzword and lot of companies think that people can take the "magic innovation pill" and they becomes a master of innovation. I faced it. What we worked on is change the culture (one of the business architecture variable) mainly top management culture, about to innovate people must be motivated and must have free time and leisure time to be innovative. Every person in this world is innovative. Why? Becasue they need to survive. But you have to give them time. Saving Changes...
I know it might be a bit late, but I think it might be worthwhile to do a pros/cons list for implementing a KM initiative. I've found KM to be useless unless you have the volume and leadership willing to push for it.