re: Can the directory be integrated into the main site search plugin functions?
Sorry, no, this is not possible because the WordPress search is only able to search posts and pages and custom post types [CTP (requires code a a plugin to enable)].
re: we are currently using “Company Directory Pro” and have been having issues with the CSV upload process. How does “Connections” compare?
Actually, I do not know since I have never used it. Glancing over their plugin page. I would say Connections is more feature filled than the Company Directory Pro plugin. Seems like it might work with SearchWP because it looks like it might use a CTP to save the contact details. Connections uses custom tables with a db schema more optimized for directory vs. CPT which are optimized for post/page content. Which is one reason Connections can not integrate into the core WordPress search.
I hope I have answered your questions thoroughly!