Yes it does. Additionally if your service has more than 1 instance then Kontena will replace each instance one-by-one when deploying. You can even define that Kontena will wait for given port before moving to next instance.
Thanks!
Edit: btw, you should probably advertise this more on the home page, I'm pretty sure zero downtime is a big no go for many when it comes to docker-compose, especially rails users used to it with unicorn.
And thanks for feedback, it is always appreciated and motivating us to make it better!