Likely it would be. But really Docker is more about convenience of deployment and (much) less about security. I would not run seriously untrusted code in merely a (Docker) container; I don't know much about the isolation guarantees of OpenVZ.

In any case, containers share OS kernel, OS page cache, etc. This can be beneficial even for a shared hosting as a way to offer a wide range of preinstalled software as ro-mounted into the container's file tree. Likely code pages of software started this way would also be shared.