In the original Broadway production of Maurine Watkins' non-musical play Chicago, Mary Sunshine was played by the highly respected (and prolific) character actress Eda Heinemann. Heinemann actually had 40 Broadway credits from '08 to '63, including Ah, Wilderness! (as Lily Miller), Watch on the Rhine (as Anise), Goodbye, My Fancy (as Miss Shackleford), Arms and the Girl (as Prudence), Make a Wish (as Dr. Didier), Graham Greene's The Potting Shed (as Mrs. Potter), and Robert Anderson's Silent Night, Lonely Night (as Mae).
In the '42 film version titled Roxie Hart, Mary Sunshine was played by Spring Byington. I've seen the film a few times. Byington's portrayal worked fine.