This paper investigates the operational implications and policy impacts of virtual triage adoption within the acute care service setting. A central problem in this context is patients' (in)ability to self-triage accurately, a notable contributor to emergency department overcrowding and treatment delays. While traditional triage solutions, such as phone services, can mitigate these issues to an extent, they struggle with accessibility and accuracy problems. However, recent advances in predictive technology have led to the development and deployment of virtual triage tools, which offer immediate, cost-effective, and potentially more accurate triage recommendations. Despite their potential benefits and increasing adoption, the impact of virtual triage tools on acute care systems remains poorly understood. This paper therefore develops a queueing game model to examine how virtual triage influences patient behavior and system performance, and explores policy actions that maximize the operational advantages of these tools. The analysis uncovers an inherent trade-off between informativeness and volume with respect to patient's compliance with virtual triage recommendations. For system performance, we demonstrate potential drawbacks of off-the-shelf virtual triage solutions, and explore the ways in which these technologies can be customized to specific contexts in order to unlock their full potential. Our findings underline the pressing need for effective regulation and thorough assessment of operational consequences to harness the full potential of virtual triage in improving the delivery of acute care.