Jason,
I don't think that will work because business events don't interact with a specific user session. The consuming app would need to create authentication information in the users browser to provide a login, however, these events run in the server infrastructure, not in a browser.
It sounds like you are looking for a single sign on capability. There are a number of those available for Mendix applications. Have you evaluated any of those? If so, perhaps sharing the gaps you identified with those would be helpful in getting some input from the community.
Hope that helps,
Mike