Yes, that's how the DD->CW integration works.
Side note: even if you shut down every service in the account, if something outside of AWS is connected to it, like Datadog, you will still incur charges. I'd recommend deleting the account if you can.
Side note: even if you shut down every service in the account, if something outside of AWS is connected to it, like Datadog, you will still incur charges. I'd recommend deleting the account if you can.
I have no idea how DataDog integration works but if I had to guess I'd expect to setup an IAM account for them to use? If so, you could delete the IAM account they're using.