According to http://maven.apache.org/plugins/maven-site-plugin/examples/adding-deploy-protocol.html is should be possible to add additional wagon provider as a dependency to the site plugin. For a project deploying via dav, doing so using the wagon-webdav-jackrabbit makes Maven through a NoClassDefFoundError. Of adding the wagon as a global extension it works.
Not sure if this is a maven-site-plugin issue though, or possible something in the specific wagon.
I'm attaching a test project as well as the console output showing the error.