Not specifically. Really it's up to your application. The only thing Kubernetes can control is what the initial command run inside the container is and there can only be one of those.

Yes, if you provide a command and/or its args, it overrides the original image's Entrypoint and/or Cmd. If you want to know how exactly it happens, please refer to this fragment of the official kubernetes docs.

If you want to run some additional command immediatelly after your Pod startup, you can do it with a postStart handler, which usage is presented in this example:

apiVersion: v1
kind: Pod
metadata:
  name: lifecycle-demo
spec:
  containers:
  - name: lifecycle-demo-container
    image: nginx
    lifecycle:
      postStart:
        exec:
          command: ["/bin/sh", "-c", "echo Hello from the postStart handler > /usr/share/message"]
      preStop:
        exec:
          command: ["/bin/sh","-c","nginx -s quit; while killall -0 nginx; do sleep 1; done"]