No, Dook is an East team because the ACC has always been an East conference.
I think they mix and match. As I recall, Duke was the #2 overall seed back in 2010 (Kansas was #1) with both Syracuse and Houston regions available to them and they went to the Houston Regional. The fourth #1 seed Kentucky got the Syracuse Regional.
Back in 2009 UNC and Pitt were 2/3 or 3/2 (not sure which) and Pitt got the East Region in Boston and UNC went to Memphis.