I don’t see any dedicated event for this but you can probably use Prototype v1.7.3 API documentation | Ajax.Responders to catch the AJAX requests that are being sent using Prototype.js (which is used by the search suggest), filter those coming from the search suggest and extract the search keywords from the request parameters.
You could listen to xwiki:suggest:updated and count the results in the DOM. See https://github.com/xwiki/xwiki-platform/blob/master/xwiki-platform-core/xwiki-platform-web/src/main/webapp/resources/uicomponents/suggest/suggest.js#L656 .