Steven Zahm@ Axel
No, Connections does not integrate with the core WP search since it is specialized. This is why it has its own search.
A “blank result” for the page with the [connections] shortcode on it would be expected if the shortcode is the only content on the page because WP does not render shortcodes in the search result summary results. The page title should still be shown plus what ever page meta the theme shows as part of the search results.
Clicking thru on the page title in the search summary results should take you to the page and the directory show up as normal, not a blank page. Is it here that you are getting a blank page? If that is the case, that does not seem like a Connections issue. Clicking the page link from the search results should be no different from clicking the page link from the site nav.
That email address, doesn’t sound like that is being output by Connections to me, but coming from somewhere else.
Its really hard to say what the issue is and what the solution will be without being able to see it… can you attached screen captures showing the Connections page in the search results and what it looks like after you click thru to the page?