I use a HttpClient that only supports async methods. Do I have to await them in the calling method (not in the async method itself, I have to await the
No, nothing requires you to await the call. The call is just returning a Task to you, rather than a T directly. If you call the Result property on the Task:
var result = client.MakeCallAsync().Result;
You are telling it "I don't care if it blocks, I want my code (and this thread) to wait here till this is done."