You can do that. If you don't await an async call, you have a future object that you can handle however you want.
The sync code might be running in an async context. Your async context might only have one thread. The task you're waiting for can never start because the thread is waiting for it to finish. Boom, you're deadlocked.
Async/await runtimes will handle this because awaiting frees the thread. So, the obvious thing to do is to await but then it gets blamed for being viral.
Obviously busy waiting in a single threaded sync context will also explode tho...