I definitely know of FacetWP, but to the best of my knowledge it only support searching WordPress pages/posts (including custom post types). Connections does not use these to store its data it uses custom tables with a schema more optimized for directories. The WordPress posts (CPT) are optimized for post like content. So adding support to Connections for FacetWP is not likely possible.
The closest I can offer is something like this:
This site uses a custom multiple category search which includes a radius search base on zipcode and a keyword search. If you think this will meet your needs I can offer it at a reasonable rate which would include installation and configuration.
Hope this thoroughly answers your question, let me know.