It does work. There are several configurations that can be made on the source endpoint (DocumentDB) depending on how you want to have the data in the target database.
For example, if the document metadata mode is selected, then this document:
rs0:PRIMARY> db.docdbcollection.find()
{ "_id" : ObjectId("62444bd3a8f382958e5b58b9"), "name" : "foo", "age" : 25 }
will be saved in PostgreSQL as:
postgres=> select * from mydb.docdbcollection;
_doc
-----------------------------------------------------------------------------------
{ "_id" : { "$oid" : "62444bd3a8f382958e5b58b9" }, "name" : "foo", "age" : 25.0 }
(1 row)
If the metadata mode table is chosen, then DMS will extract the keys and write them as columns on target, ending up with something like this:
postgres=> select * from mydb.docdbcollection;
oid__id | name | age
--------------------------+------+-----
62444bd3a8f382958e5b58b9 | foo | 25
(1 row)