Heterogeneous scientific workflows consist of numerous types of tasks and dependencies between them. Middleware capable of scheduling and submitting different task types across heterogeneous platforms must permit asynchronous execution of tasks for improved resource utilization, task throughput, and reduced makespan. In this paper we present an analysis of an important class of heterogeneous workflows, viz., AI-driven HPC workflows, to investigate asynchronous task execution requirements and properties. We model the degree of asynchronicity permitted for arbitrary workflows, and propose key metrics that can be used to determine qualitative benefits when employing asynchronous execution. Our experiments represent important scientific drivers, are performed at scale on Summit, and performance enhancements due to asynchronous execution are consistent with our model.