It should be possible now to send a Discourse invite when a member is created on Ghost. This topic outlines how to do it: Automate sending Discourse invite emails with Zapier. The only difference will be that you’ll need to select Ghost, instead of WordPress for the trigger step.
It would be good to get the ablility to send an invite added to the official Discourse Zapier integration. That would make it a lot simpler to configure sending invites with Zapier. The only action it currently supports is creating a post. Another action I’d like to see is the ability to add a user to a Discourse group.