Does anybody ships OCaml software to end users/customers using containers/docker?

I do. Though I recently met a lot of various problems considering use of the modern OCaml versions. Gladly, they all are fixed now. I base my containers on a multistage build images, using Alpine Linux, and then copy the statically-built files. To save some precious bytes (and CPU usage) you can also build a static binaries inside these Alpine Linux containers and just copy the resulting binary out of the container. I do so in some cases.

Apart from Nix you might also consider Guix, see for example, their new guix deploy feature.

In some discussion before I wrote a few benefits of Guix compared to Nix: