Self-supervised foundation models have recently been successfully extended to encode three-dimensional (3D) computed tomography (CT) images, with excellent performance across several downstream tasks, such as intracranial hemorrhage detection and lung cancer risk forecasting. However, as self-supervised models learn from complex data distributions, questions arise concerning whether these embeddings capture demographic information, such as age, sex, or race. Using the National Lung Screening Trial (NLST) dataset, which contains 3D CT images and demographic data, we evaluated a range of classifiers: softmax regression, linear regression, linear support vector machine, random forest, and decision tree, to predict sex, race, and age of the patients in the images. Our results indicate that the embeddings effectively encoded age and sex information, with a linear regression model achieving a root mean square error (RMSE) of 3.8 years for age prediction and a softmax regression model attaining an AUC of 0.998 for sex classification. Race prediction was less effective, with an AUC of 0.878. These findings suggest a detailed exploration into the information encoded in self-supervised learning frameworks is needed to help ensure fair, responsible, and patient privacy-protected healthcare AI.