I fix computers to get a little extra money. I'm planning to buy a removable hard drive to carry important programs and stuff and I'd like to install Ubuntu 11.04 in it too. So, I can't install proprietary graphic drivers in it, so Unity 3D is out of question.
Can I run GNOME Shell without installing drivers when I boot it in a Nvidia or ATI graphics computer?
Both gnome-shell and Unity will require compositing in order to be used. You can install proprietary drivers and still have it on a USB/external drive - I do it all the time and move from computer to computer. Besides, you can always install the Gallium3d drivers for Nouveau and you'll have fully-supported 3d on all the important cards.
Both Unity and Gnome-shell are anything but out of the question.
Yes, it will need compositing, however there is a fallback. From the GNOME3 FAQ:
Yes, open-source ATI drivers already provide 3D acceleration, and open-source "Nouveau" driver will provide 3D acceleration for Nvidia cards in Natty. It means that even Unity 3D and GNOME-Shell are likely to be usable. Moreover, you can install Unity 2D from Ubuntu repository (it's not included by default), it has almost the same functionality as its 3D equivalent and runs on even broader range of hardware.