Alzheimer's disease (AD) is the fifth-leading cause of death among Americans aged 65 and older. Screening and early detection of AD and related dementias (ADRD) are critical for timely intervention and for identifying clinical trial participants. The widespread adoption of electronic health records (EHRs) offers an important resource for developing ADRD screening tools such as machine learning based predictive models. Recent advancements in large language models (LLMs) demonstrate their unprecedented capability of encoding knowledge and performing reasoning, which offers them strong potential for enhancing risk prediction. This paper proposes a novel pipeline that augments risk prediction by leveraging the few-shot inference power of LLMs to make predictions on cases where traditional supervised learning methods (SLs) may not excel. Specifically, we develop a collaborative pipeline that combines SLs and LLMs via a confidence-driven decision-making mechanism, leveraging the strengths of SLs in clear-cut cases and LLMs in more complex scenarios. We evaluate this pipeline using a real-world EHR data warehouse from Oregon Health \& Science University (OHSU) Hospital, encompassing EHRs from over 2.5 million patients and more than 20 million patient encounters. Our results show that our proposed approach effectively combines the power of SLs and LLMs, offering significant improvements in predictive performance. This advancement holds promise for revolutionizing ADRD screening and early detection practices, with potential implications for better strategies of patient management and thus improving healthcare.