Can the C# compiler distinguish between I/O bound and computational tasks?

Consider a snippet of code such as this:

public async Task<Bitmap> DownloadDataAndRenderImageAsync(
    CancellationToken cancellationToken)
{
    var imageData = await DownloadImageDataAsync(cancellationToken);
    return await RenderAsync(imageData, cancellationToken);
}

The first of the steps in this method is I/O bound work where as the second, computational.

When we rely on the compiler to generate the right task-based code for this asynchronous operation, what does the compiler do?

Specifically, does it know that the first one is I/O bound so it must use the TaskCompletionSource<T> class so that there is no affinity between a thread and the task, and that for the second one, it can use any of the methods such as Run or StartNew or Start to schedule the task on a thread-pool thread?