Not yet, but that's coming very soon. We've been artificially limiting the number of architectures supported to limit the headache of managing cross-arch container images. We're reaching the point where that will no longer be a problem - meanwhile the Docker on Raspberry Pi community is growing restless and we want to make them happy :)
The boundary between "kernel" and "libraries like libc" is very stable and doesn't change often. That means that often, the kernel distributed by Arch can work reasonably well in an Ubuntu system, and vice versa.
With that in mind: The "ubuntu" image ships the "ubuntu-glibc" and "ubuntu-bash" and "ubuntu-coreutils" and so on, but they continue to work on your Arch host because the system calls don't ever change.
You can't link (say) ubuntu-glibc into arch-bash though, which is why containers are built off of a "base ubuntu image" in the first place.
Containers come with their libraries though; you don't have to "add" anything. You'd just apt-get it within the container and it would pull down its dependencies.
This, by the way, is the reason we artificially prevent docker from running on multiple archs. If half of the containers you download end up not running on your arch, and there's no elegant way for you to manage that by filtering your results, and producing the same build for multiple archs (and what does it even mean to do that?) - then all of sudden using docker would become much more frustrating.
This sounds like a clothing manufacturer who only makes clothes in black because trying to match colors would be too frustrating for customers. At the end of the day, lots of people have multiarch networks, and don't want to have to choose between using a tool or supporting just one platform. Removing functionality does not make their lives easier.