Fact: Nope. In fact, the details of this supposed affair didn't come around until after Spencer was dead --- Kate herself spread them about. During the 27 years, not even the press suspected anything more then just friendship. Well, that's because their affair only lasted 5 years. At the most. Spencer frequently had on-set affairs, and drank heavily. He fit her need to play caretaker, so she took advantage of this and took care of him without being tied down.
You can learn more by visiting the Tracy & Hepburn portion of this site.
Myth: Katharine had secretly had children.
Fact: Everybody knows that after child birth, a woman's body is never the same. Kath's figure never changed until she was much older and well past her child-bearing years, but even then she was still slim.