Hi
I was looking for an answer to this myself, would be interested to know if you have an answer.
I think that the problem is that all sites in the network have their own database tables. That means that anything that is using a custom post type will be storing that info in the posts and associated tables for that site so any form will be unique to the site.
I have happily created two sites and created two contact forms which the shortcodes can handle.
Whilst I have only just started looking into this my gut feeling is that there is probably a way to hook into the code for CF7 and auto-create a form, after all they do this when the plugin is activated. My other gut feeling is that this will be a right pain to get done and will not be a quick job.
Andrew