Yeah, single core/dual core... Doesn't matter. They both can address that much RAM. It's possible that what your friend meant is that with a single core processor it can't do that much at the same time anyways, so even if you did add the RAM, it wouldn't have a huge effect on performance.
I suppose that would be true to a very small degree, but even still, the biggest thing is that the computer won't have to be constantly running back to the harddrive every time you wanted to access another program. For that reason, extra memory will have an impact, especially with the likes of Photoshop.
Still, I wouldn't invest in that machine. You'd still be able to sell it for good money and then take what you would have spent on extra RAM and get a more capable machine.