Это работает.
WebClient wc = new WebClient();
string result;
Task<string> downloadTask = wc.DownloadStringTaskAsync(new Uri("http://badurl"));
downloadTask = downloadTask.ContinueWith(
t => {
return wc.DownloadStringTaskAsync(new Uri("http://google.com/")).Result;
}, TaskContinuationOptions.OnlyOnFaulted);
result = await downloadTask;