Well, yes and no. According to History.com, in 1936, Ball registered to vote and listed an affiliation with the Communist party as other family members had. Ball explained later that she did so to “appease her socialist grandfather.” However, the site states Ball never achieved active member status. As far as I've seen she's not known for communist or socialist statements or activism.

She was rather lucky really she became pregnant at the time the story broke of her being a communist so it got “covered up” but like Karlboll says she only did it for her grandpa she loved him and she was young and just did it to make him happy.

Happy to hear that she wasn’t a Basie :)