@ Larry
The only WordPress directory related project that integrate with the core WP search are directory themes. All the plugins that I’m aware of and at the last time I checked them out; do not integrate with the core WP search. Likely for the same reasons. Currently, I do not know if WordPress provides the necessary hooks to accomplish this. If it does, there is a huge challenge in how to commingle the post search results with directory search results that would be of benefit to the end user. I will very likely continue to improve the searching feature within Connections rather than investing that time in integration because it is very seldom requested.
Integration with the core WP search has no relation to Google’s ability to index your site. I’ve built many SEO items into the core of Connections to entice the Googlebot to index the content and I will be adding more such as changing the markup from hCard (which is still supported by search engine) to the new and preferred Schema.org markup; altering the page creation date and last modification date to match those details when clicked thru to a single entry. Addiotnally, if the WordPress SEO by Yoast plugin supports it, injecting the Connections data into the sitemap it creates for search engines. Ultimately though, it is up to the Googlebot if it will crawl the pages and if it index it to return as search results.