On the link above there is a separate section for billing account suspensions and it seems to work how you described.
You can fairly easily swap billing accounts a project is using if you still have an organisation admin account that isn't suspended. I saw this risk coming at a previous company and tried to get them to treat billing accounts like any other important resource and go for redundancy, but the director could not see the value and our Google account manager denied the risk existed, luckily they have been more fortunate and this has not happened to them yet, although it did come close once with some issues with the payments.
You can fairly easily swap billing accounts a project is using if you still have an organisation admin account that isn't suspended. I saw this risk coming at a previous company and tried to get them to treat billing accounts like any other important resource and go for redundancy, but the director could not see the value and our Google account manager denied the risk existed, luckily they have been more fortunate and this has not happened to them yet, although it did come close once with some issues with the payments.