No, the computer will run without an OS, you just won't be able to do anything on it. The operating system is required to make software applications and services functional by having a platform to be launched from.
You can purchase Windows as a download, rather than as a physical disk, but you would need another computer to do it and would still need to burn it to either a disk or copy it to a USB device. The disk is probably the better method as that way you have the actual product to install from in the future if you have to reinstall, plus you can always make a system image on usb or hard drive space for restoring in the event of a later problem.
Here is a tutorial on what you will need to do once you have the disk. You will also probably need to install additional drivers for your hardware after installing the OS and updating windows with windows update is highly recommended after a clean install as well.
http://www.eightforums.com/tutorials/2299-clean-install-windows-8-a.html