IIUC (someone please correct me if I've misunderstood), this is essentially an implementation detail of the underlying operating system/scheduler/runtime. When a suspension point is reached, Swift will yield the thread back to the scheduler, and at some point in the future the rest of the async function will be scheduled to run.
In UIKit-land, this would (I assume) mean handing control back to the main RunLoop so that it can continue to service UI events until the rest of the async task is ready to run.
As for the chicken-egg problem with async function calls, there have been a couple solutions mentioned which will allow non-async functions to spawn async execution contexts.