Since Android uses the Linux kernel, if you have full access to the device, you can already generally sideload a distribution of your choice onto the filesystem. The Linux userspace can run and coexist alongside the Android userspace. Though some applications may require kernel features which are not enabled in typical Android kernels, GPL forces manufacturers to release the kernel source code, which makes it fairly easy to enable more features and use that kernel.

The advantage of this approach over running Linux in a sandbox / VM is that you can administer your Android device from the Linux side, which means that you can use your existing backup strategy or other automation tools. With a USB/bluetooth keyboard, it can also work as a small PC in your pocket.