Would this graphics card work

it depends on your other specs. Test Drive Unlimited - easily, NBA 2k12 - sure, but GTA need a good processor. If yours is decent, sure, otherwise, not really.

I have a Intel Pentium which runs at 2.27GHz dual core

I have a Intel Pentium which runs at 2.27GHz dual core

Well, it meets minimum requirements barely, but should be OK on low settings. Don't expect more than that.

Mistake it runs at 2.70ghz

Any idea of the model? Because they started producing dual core pentiums back in 2005, and they still do. Clock speed says little, because architecture improved, and at same clock speed they are about 3 times faster than they were 5 years ago. 2.7 GHz suggests its a more recent model, and if it's G630, it will run GTA easily on high settings with HD 6670.