Ok, so just to be clear here, HDFS is not a DB -- it's a distributed filesystem. But if you do use the GCS Connector to use GCS as HDFS, that I believe is only for the final output. Your Dataproc nodes still have HDD/SSD provisioned on them which is used for intermediate read/writes by the job you're running.
Using GCS as an HDFS alternative allows you to shutdown your Dataproc clusters when you don't need it and still retain the data. Traditional HDFS is spread out over multiple machines (hence the "distributed" in its name) so you would have to leave machines running to maintain that HDFS.