Still thinking through requirements regarding integration. Would love to work with other users to come up with full requirements.
Their forums are not very good. No threading so nobody knows who is talking to whom, no real back-end controls, no usernames, no merging, hiding or trust levels. It is not viable to even a moderately active community.
We were mostly focused on extending support to our users through private message, linking posts to tickets or creating tickets from posts. What you want may be able to be done by simple web-hooks.
I think there should be a plugin in Discourse and a channel app in Zendesk. I just need to flesh this out more before going to the community to sponsor a build.