I had a quick look, but I don't think we have integrated this yet.
On their website they mention multiple output possibilities.
https://www.elastic.co/guide/en/logstash/current/output-plugins.html
The one that looks most promising to me is the HTTP output plugin, which should allow Logstash messages to be sent to a HTTP endpoint.
https://www.elastic.co/guide/en/logstash/current/plugins-outputs-http.html

Further investigation would be needed.