I know it isn't in Apple's list of supported Macs, but I want to know if anyone has tried it.
Also, my Mac has 4GB of ram and plenty of disk space. It currently runs Lion.
As Steve Moser says there is no support for 32 bit drivers and Mountain Lion will refuse to install on the macs which had 32 bits drivers (someone seems to be too lazy to rewrite them?).
If this answer is not the one you want to hear, then you can install Mountain Lion the hard way. Because there is a way (which worked for the preview).
You will need another compatible mac (support) and you will have to do some hard drive switching.
The idea goes as follow:
You should be able to get to the desktop but without hardware graphics support.
To enable the graphics hardware support you will have to install the right kernel extentions. You could use kexthelper.
EDIT: To avoid all the hard drive switching and messing with internal components you can boot the target Mac in the so conveniently named "target mode" and connect it to the support Mac on which you could install the OS to the target drive and then boot on the target drive to edit the plist files.
No, Mountain Lion requires 64-bit graphics drivers and mac formatted drivers don't exist for the graphics in the early 2008 White MacBook.