The White House is Seeking Entrepreneurs for Presidential Innovation Fellowship

There's actually already work being done much like what you describe and it involved the first two rounds of Presidential Innovation Fellows - both to help shape the policy and to facilitate implementation. I'm referring to Project Open Data (http://project-open-data.github.io/) which is backed by an Executive Order to get every major federal agency to catalog all their data assets including those that are not and cannot be public. This full inventory is referred to as the Enterprise Data Inventory (EDI) while the portion of that covering anything that should legally be public is called the Public Data Listing (PDL). Every agency subject to this law is required to post their public listing in a standardized json file at the root of their agency website. The PDL is not only meant to point to datasets that are already publicly available, but it also requires agencies to list datasets that should be public, but have not yet been released or are not yet online. The datasets that are not legally meant to be public must be included in the EDI, but it's up to the discretion of the agency whether they want to list any in their public PDL. Some agencies have been doing that though. Otherwise, the full EDI with an accounting of all non-public datasets will really only be overseen by the White House Office of Manage and Budget and it's up to them to determine what kind of information they'll release about the EDI's they receive from agencies.

As agencies continue to release their Public Data Listings you should be able to find metrics about this at https://www.data.gov/metrics In the future that site should also include metrics like the number of unreleased datasets listed in their PDL data.json file.

An interesting idea. I doubt any one Fellow has the power to do that, however, Round 3 does have a lot of Open Data Initiatives which might be related to this.