Does it work with page caching?

Yes. The buttons are plain HTML with no per-visitor content, so a cached page is a correct page. Counting happens in the browser after the click, so it is unaffected by the cache. Saving a change visitors would see empties the caching plugins it knows (see "After a change" in the documentation), so cached pages show it too, and so does each update of the plugin, once. Switching the plugin off on a site empties them too, and switching it back on empties them once more. A host's own cache or a CDN may need clearing by hand.