Mendix will have a database. You would use it eg to store access data to make sure not everyone can just call the API, but you don't need to store the data retrieved from the API in it. The strength would be to use the relational structure of the data/domain model combined with the out of the box capabilities for REST API connections.  You can use so called non persistable objects to work with the data in memory only. When the user session is closed the transactional data is removed as well.