My understanding (usual caveats of "could be wrong" here) is that ORM solutions do not work with Object Oriented databases, as OO databases remove the need for the ORM solution.
In general, an ORM is used to help abstract the relational model, and abstract away from the logic of the code the mismatch of the relational model to the object-oriented system. It also allows for usage of traditional databases that are often required for legacy systems to continue working, but gives you the freedom to handle the relationships in a OO fashion.
The abstraction is the real benefit, imo, of using an ORM. Swapping database vendors is not as easy as some would make it out to be, especially is you are switching from or to a database like Oracle, where there are lots of custom operations and custom behavior in the JDBC drivers.
Another element to your question is that it is unlikely that you would want to use the same baseline database model from a relational database to an object-oriented database. I would think that such a paradigm shift would recommend, if not require, a rethinking of the logic and connection behavior of the underlying core system.