Well I have some good news and some bad:
Your system is on the edge of being supported. In reviewing this TN your system makes the grade running Lion - Systems that support Lion.
But, Apple created a new TN for Mountain Lion - Systems that Support Mountain Lion which clearly implies it is not supported.
I think Apple is looking at its stock build of this system. If you review the other supported systems you will note they have larger hard drives (yours 80GB the others 120GB or bigger).
The other fact here is both Lion & Mountain Lion need more memory than what your system has. Your system can only offer the OS & Apps a max of 3GB using 2 - 2GB memory modules which is on the lower end of what I would recommend (surfing, iTunes, light app use...)
So you'll need to upgrade both and then your limited to Lion by Apples TN. I still think you can upgrade to Mountain Lion on this system (if you've done all of the needed hardware upgrades) but then again I've not tried it.
So it all comes down to costs and risks - I still think you should consider buying a newer system than trying to do all of the upgrades (check out all of the costs Vs a used system) knowing Apple won't support anything higher than Lion on it.