I have gotten multiple queries on this. Yes, it is possible to run Windows Memory Diagnostic without installing Vista!
You can do it through the Windows installation disc. To run memory diagnostic, insert the installation disc in the computer and reboot. When you get the prompt "Press any key to boot from CD or DVD..." press and hold the SPACE BAR or tap it multiple times. This should bring up the Windows boot manager menu that lists Windows Memory Diagnostic as an advanced tool. Hit the TAB key to select Windows Memory Diagnostic and then hit ENTER to run it.
After Memory Diagnostic is done, the machine will continue booting into the installation disc.