No, ES versions 6.8.9+ and 7.8+ are not affected by this as stated in community post:
Supported versions of Elasticsearch (6.8.9+, 7.8+) used with recent versions of the JDK (JDK9+) are not susceptible to either remote code execution or information leakage. This is due to Elasticsearch’s usage of the Java Security Manager. Most other versions (5.6.11+, 6.4.0+ and 7.0.0+) can be protected via a simple JVM property change. The information leak vulnerability does not permit access to data within the Elasticsearch cluster. We have released Elasticsearch 7.16.1 and 6.8.21 which contain the JVM property by default and remove certain components of Log4j out of an abundance of caution. This is applicable to both CVE-2021-44228 and CVE-2021-45046. Elasticsearch has no known vulnerabilities to CVE-2021-45105.
On December 19th we released 7.16.2 and 6.8.22 which include the most recent version of Log4j (2.17.0).
The full post can be found here: Apache Log4j2 Remote Code Execution (RCE) Vulnerability