No, as @dragonsh said, Kubernetes will be a bad choice for you. Kubernetes is complex, specially its network stack, you'll need to setup an VPN from each site to your control plane site to keep some basic functionality working (kubectl logs, for example).

If you don't care about a centralized API to probe status and manage each instance, Ansible should be enough to orchestrate these installations and with little effort (that also depends on the application at hand) getting zero-downtime rollouts with Docker can be easily done with it.

However, if you want a single control place to probe status and want to avoid writing your own rollout scripts, Hashicorp's Nomad [1] might be a good solution for this. It is a lot simpler than Kubernetes while still giving you nice primitives to describe jobs/services, health checks, rollouts strategies and etc. Treat every site as a datacenter of its own, setup a job of type "system" (akin to Kubernetes DaemonSets) and all you need on these sites is internet access to your HTTPS endpoint of the Nomad control plane.

If you want to talk more about this, hit me up on Twitter or Telegram, I use @rochacon as my handle virtually everywhere.

[1] https://www.nomadproject.io

Edit: grammar and typos