You may configure Artifactory to allow un-authenticated ping to the server by using steps below:
1. Set artifactory.ping.allowUnauthenticated=true in artifactory.system.properties
2. Restart all artifactory nodes
Then create an http check from the ELB towards the server on the correct port and path (/artifactory/api/system/ping). With such a setup, ping is only expected to return OK when the server is ready, and in that way the node would not be brought back into play unless ping is ready.
Alternatively, you may configure a TCP healthcheck which checks response on the artifactory node (default 8081), and add enough checks and time between intervals to assume readiness between the time tomcat is launched and until Artifactory is ready.
More details regarding ELB health check configurations can be found here: http://docs.aws.amazon.com/elasticloadbalancing/latest/classic/elb-healthchecks.html