Probably not unless you have the absolute best tile person in the world.

If he really wants to install white tiles on the floor, at least keep the grout color matched or similar to the tile.... You're correct to be leery, as dark colored grout combined with a white tile will look cheesy/lousy in most cases, in addition to the intricacy of the herring bone pattern install. I'd start with your shower/wall tiles first, after they're fully installed, you'll have a lot better idea of what to color coordinate for when choosing for your flooring tile... Good luck !