Does Airflow Kubernetes Executor run any operator?
Kubernetes executor will work with all operators.
Using the kubernetes executor will create a worker pod for every task instead of using the celery worker as the celery executor will.
Using the KubernetesPodOperator will pull any specific image to launch a pod and execute your task.
So if you are to use the KubernetesPodOperator with the KubernetesExecutor, Airflow will launch a worker pod for your task, and that task will launch a pod and monitor its execution. 2 pods for 1 task.
If you use a BashOperator with the KubernetesExecutor, Airflow will launch a worker pod and execute bash commands on that worker pod. 1 pod for 1 task.