Yes, in principle, you can use docx4j to convert binary .doc to OpenXML .docx.
HOWEVER, this is more of a basic proof of concept, as opposed to something which will handle a wide range of real world documents.
The issues are two:
1. it uses Apache's POI to read the binary doc, and POI is quite limited in its handling of Word documents (which it calls HWPF)
2. and then for each feature POI can handle, we need to write support for creating a corresponding docx4j object
Currently, Doc.java has basic support for paragraphs and tables.
Have you looked at http://b2xtranslator.sourceforge.net/blog/
? That is written in C#, but it is open source.