You can use ArcGIS Online Assistant to migrate the web maps & web apps only if personal non-organizational account as storing hosted services is not possible without an organizational accounts. You will be able to add the hosted services as an item which reference the original service. That being said if they site goes down or the original service is dropped your item, web maps & the web apps will stop working.
However, you use AGOL Assistant if you want to migrate all the data to another Organizational account.
Regards,
~Shan
~Shan