Obviously, Android runs applications in sandboxed mode for security reasons, but if I have root and shell access on an Android device, can I then treat it as a regular linux distro, and run any program that I am able to download and install (assuming architecture/hardware compatibility)? Does Android have any system or kernel level limitations that would restrict certain things, or make it incompatible with common desktop linux distros?
EDIT: Indeed, my question wasn't written very well. Let me be more specific:
Can I run any natively compiled code, as long as it is compatible with the hardware architecture?