Give it a try?
Core2duo is the bottom line for ok Windows 7 performance and was standard in 2009 when Windows 7 was released. It is tuned for that cpu as the icore's came out just afterwards. Pentium IV's I would not bother but people have successfully ran it on them believe it or not.
Also Windows XP has no hardware acceleration anyway. GDI is not GDI+ like in Windows Vista and higher. IE 9 was very usable on this system with hardware acceleration on. Just flickered a little as long as no more than 1 ad or flash video was on it was ok.
Windows7 is the new XP and will be used for many years to come. My father has a core2duo with an intel gma 945 chipset. I put Windows 7 on it for him last summer. It works. It has 2 gigs of ram and occasionally it can get slowed down with hardware accelerated flash ads if you has more than 4 tabs opened. But for his needs it is fine.
Yes he would still be using XP today if I didn't upgrade him. There was no reason to change other than security issues. So I can see why many still use that aging OS. Baby boomers make up a significant part of the population. Corporations too are very cheap and see no point in upgrading and spending lots of money and increasing risk for something that does what they alread have?!
They will wait until 2019 to even start upgrading today and blame MS and not themselves as usual.