In your application the JSF View components will be used in Screen rendering(View)
All the request parameters will come to JSF Backing Bean which is a controller here.
And MySql or XML Database related work will be in Model Layer.
So as long as XML Database Specific Java Api is available for communication with eXist-db you can integrate that in model layer of your application.
You can have help in
http://exist-db.org/exist/apps/doc/devguide_xmldb.xml
So in Model Layer of your JSF based Java EE application you can integrate it easily.