Yes, the analytics and click analytics search parameters are separate.
If you set analytics as false (which means that the search will not appear in your analytics) you can still set clickAnalytics as true, and use the search to send events.
However this click event will not be tracked in your analytics, because there will be no search in your analytics to link it back to. As there will be no search information, the events can be used for Algolia Recommend or Personalization but they will not work with NeuralSearch, Dynamic Re-Ranking, Query Categorisation or A/B Testing which all require events to be linked to a search.