Re: Calling Android a "Linux distribution" is entirely misleading.
You have some things in your post here that are technically incorrect. You should be aware that Android and GNU cannot coexist in the same root directory. In order to run both on the same device (even when they are both compiled for ARM or both compiled for x86) they need to each have their own root directory. This can be accomplished by installing them to different partitions or using a chroot jail or some other type of container.
There are several applications that have been ported to Android from GNU/Linux, and they can come in handy when you are in Android. I have run a GNU/Linux distribution on a number of ARM devices, and the executables for those cannot run inside of an Android environment. I have run Android and GNU/Linux on the same device, and you cannot run an executable for one system in the other even when you are running the same kernel for both systems (each time I did this I was running the same kernel for both systems; I don't mean two copies of the same kernel; I mean the same exact kernel).