No. The other Harrison Ford. No relation. Madge Bellamy described herself as "an athiest, vegetarian, and a leftist." Took a fleet of publicity men to keep that under wraps, I suspect. She earned the studio's ire whe she refused to do a film Fox had crafted especially for her, "The Trial of Mary Dugan." The role eventually went to Norma Shearer, and concerned a Broadway showgirl arrested for stabbing her rich boyfriend.

As for Madge, her career went downhill after that. In 1943, her rich boyfriend jilted her for another woman - and she shot him. Wikipedia says:

The facts of the case remain somewhat cloudy. Shortly after the shooting, Bellamy was quoted as saying, "I only winged him, which is what I meant to do. Believe me, I'm a crack shot."

The case was eventually dropped. She died in 1990, as old as the century.