Mobile health (mHealth) technologies are increasingly used in the treatment of alcohol use disorder (AUD), offering continuous remote monitoring through connected devices such as breathalyzers. These devices not only provide objective measures of alcohol consumption but also capture behavioral indicators of treatment adherence, such as timing and frequency of sample submissions. While prior studies have used machine learning (ML) models to predict relapse and dropout based on clinical registry data, few have incorporated momentary, real-world data from objective measures. This retrospective cohort study aimed to develop and evaluate predictive models for (1) treatment dropout and (2) the occurrence of a drinking event within the following 7 days, using data from 246 AUD patients enrolled in a breathalyzer-based monitoring program. Features included static demographic and clinical variables, daily breathalyzer data, and temporal trends. The dataset comprised approximately 80,000 daily observations. ML models evaluated included GLM, XGBoost, Random Forest, WildForest, and LSTM (2- and 3-layer). The best model for dropout was WildForest (ROC AUC = 0.63), based on static and trend features. For drinking events, a 3-layer LSTM incorporating all data sources over a 30-day window achieved the highest performance (ROC AUC = 0.94, F1 = 0.72). Ablation analysis revealed that variations in breath sample timing were among the most informative predictors. These findings support the feasibility of using ML models trained on breathalyzer-based monitoring data to predict clinically relevant outcomes in AUD treatment. Further analysis is required to conclude its final performance in predicting both outcome measures.