We have to do cuda 5.0 programming on Ubuntu 11.10. Since we are using a shared workstation, we have chosen to go for a external HDD installed Ubuntu. Will this ubuntu work as the normal PC version supporting the drivers and softwares?
Everything should work the same way whether ubuntu is installed on an internal or external drive.
The one thing that will make a difference is how you install it. If you install it from another computer/OS with the USB installer, you will get the "Try or install" screen on boot. This will not be exactly the same.
If you install it on the external drive, the same way you would if it were an internal one, then that is the "normal PC version". There is no difference. In fact, I've installed it on USB flash drives this way, and the only difference is that they are slower than internal hard drives. Just make sure that you choose the right drive when installing so you don't erase anything important. This includes GRUB, which should be installed on the external drive as well.