I would go so far as to suggest a company policy (or at least, a publicly announced engineering-department policy) that email may be ignored for as much as a week, and that anything that can't wait that long should use IM or phone.

I'm not thinking that most people would ignore email for that long most of the time; in practice I think most would check it once or twice a day. But sometimes people need several days uninterrupted, and they should be able to have it.