Is an asynchronous query still running if an exception is unhandled?

If an exception is left unhandled in a synchronous query, the final status is set to Error running query along with the running time.

void Main()
{
    throw new NotImplementedException();
}

But if an exception is left unhandled in an asynchronous query, the status is not updated, it's left in the Query continuing asynchronously status and is unclear if it is terminated.

async Task Main()
{
    throw new NotImplementedException();
}

Is it still running? or is the status just not being updated in this case?