Emotion detection through sensors is intrusive and expensive, making it impractical for many educational settings. As an alternative, sensor-free affect detection, which relies solely on interaction log data for machine learning models, has been explored. However, sensor-free emotion detectors have not significantly improved performance when trained solely on students' interactions with their environment. In this study, we aimed to improve the performance of these models by incorporating students' personalities as additional information during model development. Personality is known to influence emotions, and the duration of negative emotions may depend on students' personalities. Therefore, we hypothesized that including personality data, based on the big five theory, in training machine learning models for sensor-free detection would enhance their performance. We collected data and videos from students using a step-based math intelligent tutoring system and used human coders to annotate emotions as target labels for our dataset. To test our hypothesis, we compared the performance of affect detectors trained with personality data to those trained solely on interaction data (baseline model) to detect confusion, engagement, frustration, and boredom. We found that incorporating personality data provided only a modest improvement in engagement detection. Our detector detected student engagement with a Cohen's Kappa of 0.633 and an area under the curve (AUC) of 0.846 compared to Kappa = 0.630 and AUC = 0.846 for the same detector without personality data. Despite studies indicating that personality affects learning, this modest improvement leads us to conclude that adding personality information to sensor-free affect detectors is not cost-justifiable.