Yes, the plugin works in a cached environment. Because the plugin adds code to wp_footer() when it’s installed, you’ll need to clear the cache one time after the plugin is activated, but after that it should work without issue.
With the CallRail WordPress plugin, you’re only be able to add the code for a single company. If you’d like to add the code for more than one company, you’ll need to install the Dynamic Number Insertion code for each company manually in the template footer.