Actually, yeah. You can. Especially these days where consoles are basically just underpowered PCs. For example, the XBone is running a Frankenstein'ed version of Windows 8 and Windows RT. PS4 is using a modified version of FreeBSD. Neither one are strictly "off the shelf" operating systems, but neither one are completely new, either.
Last generation, Sony caused a ruckus by tangling with people who installed Linux on their PS3s for fun (and promptly learned not to tangle with the types of people who install Linux on a PS3 for fun)
So yeah, they're just computers. Really, the only difference is that you don't get the administrator/root login. You just get user credentials, with no rights or access to change anything. Imagine if you set your PC to automatically login and launch Steam's "Big Picture" view on boot up. Congratulations, you just made a console.