There are a few other places on the documentation that are imprecise or misleading for await. While the information needed is scattered around the docs, I think these can also be improved. I'm pretty sure these fit with this issue.

Developing with asyncio guide:
https://docs.python.org/3/library/asyncio-dev.html#concurrency-and-multithreading - first paragraph, "When a Task executes an await expression, the running Task gets suspended, and the event loop executes the next Task."  Taken by itself it isn't clear that execution of the awaitable starts immediately without intervention from the event loop. A possible fix might be to add "If the awaited expression is a coroutine its execution begins immediately and the  running Task will not suspend till the awaited expression stalls waiting for a result." 

The same sentence is found in the Task documentation: https://docs.python.org/3/library/asyncio-task.html#task-object