It's a nice theory, I just don't trust Everton to stick with any kind of plan.
Klopps teams definitely press, or at least they used to. It wasn't a 90 minute, rabid dog press like Bielsa in the Championship and his first season in the Premier League, it was controlled and triggered in specific areas.
Whatever people think of him, the managerial search should be down to Thelwell. The board can have input and the owner can (if he feels strongly enough) veto, but it has to be the DoF choice, otherwise, what's the point?
From the noises in the press it already seems like we have Kenwright, Thelwell and Moshiri phoning a whole host of people. It will be a good week (at least) before they get their list down to 2 or 3.