Hi Flipbit - Welcome to the site
It has been my experience that Windows 7 will need at least 512MB memory. It is preferred to have 1024MB memory or more.
12GB Hard Drive space which does not leave much space for data out of your 18GB
I have a celeron 3.2 with 1GB memory and needed to upgrade my video to run the Windows Aero feature without glitches. It is less taxing on the system with Windows Aero turned off.
However to answer your question. I do not know if it will run on a machine so old. I would recommend a Computer Upgrade or stay with XP. There are older hardware drivers for XP that will not be supported by Windows 7.