Schmidt is sitting on an advisory board, not taking a position within DoD. You can ask about the propriety of a corporate executive sitting on a board advising the civilian defense component on new and emerging technologies -- especially since Google until recently was a speculative-tech defense contractor through BosDyn -- but it's not uncommon and certainly nothing unusual to Google.

As for the OP, well, consider me skeptical of the idea that "digital government" can have a significant effect on governance itself. The problems within government agencies lie in a mix of politics, policies, processes and people, with a healthy dose of iron-triangle confusion of interests where applicable. Better digital can improve an agency's operations, but can't address whether those operations are fundamentally misguided.