I have a server running the docker container, I want him to join the existing kubernetes cluster and not affect the container that is currently running.
Because it is a production environment, I have not tried
I think k8s implementation should not impact existing docker containers within the same compute environment. As @coderanger mentioned in his answer, kubeletmanages garbage collection mechanism in order to keep system utilization on appropriate level and reduce amount of unused containers by adjusting the specific thresholds.
However, as per official k8s documentation, kubelet eviction method should not affect any containers which are not managed by k8s itself.
Mostly yes, running containers should be unaffected but the kubelet might try to clean up unused images.