Would GTA IV work with these specs? :)?

Yes, you could definitely run GTA IV on medium settings smoothly (above 50 fps). I wouldn't go crazy with higher settings than medium because of your CPU, which isn't a quad core processor. As someone pointed out already, you would need to have the recommended quad core CPU to have smooth gameplay with max graphics on GTA IV. But your graphics card definitely packs a punch, with 1GB DDR3 VRAM and DirectX 11 compatibility (almost as powerful as my laptop gfx card :D)