As others have said, it varies greatly. I've seen COOs with some focus on process/productivity improvement, but most I see are too bogged down with operational

As others have said, it varies greatly. I've seen COOs with some focus on process/productivity improvement, but most I see are too bogged down with operational details, fixing messes, vetting vendors, or a host of other things to work on that. And while they may encourage others toward deep work, in my experience COOs are very unlikely to get much deep work in themselves, so keep that in mind. What you like to do is often what consultants are brought in for. Consulting has its pros and cons, of course, and it's likely that someone with a pure engineering background will need at least significant management experience or some PM certs to look good for that. As an aside, I'm a firm believer in the idea that GTD or GTD-lite for the workplace, with meetings and project reporting focused on next-actions and an expectation that people keep up with weekly reviews, is one of the best things a company can do for itself.