Sending Exceptions to Elastic Stack via REST
It depends on what you're trying to accomplish but IMO if you're interested in reliably getting your exceptions you probably want something between Elasticsearch and your app - a queueing or logging system of some kind like Kafka or Redis.
Send your exceptions there and then drain that to Elasticsearch. Otherwise you run the risk of overwhelming ES's ability to accept writes at the very time you need it most (cascading failure, DDOS etc).