Answer:
Mark Hamill was one of seven children: two brothers, Will and Patrick, and four sisters, Terry, Jan, Jeanie, and Kim.
Mark Hamill's paternal ancestry is:
William Thomas HAMILL, Jr.
William Thomas HAMILL, Sr. (b. 1901, Colorado)
Hockley Thomas HAMILL (b. 1873, Colorado)
William Arthur HAMILL (b. 1836, England; imm. 1842)
Dorothy Hamill's paternal ancestry is:
Chalmers Martin HAMILL, Jr. (b. 1922, Ohio)
Chalmers Martin HAMILL, Sr. (b. 1884, Illinois)
Robert E HAMILL (b. 1857, Alabama; father was from Scotland)
So, the answer to this question is a qualified no, they do not have a common ancestor within the last four generations.