VRAM is a lot faster than system RAM and they don't exactly map like that. Maybe your application would allow you to choose where to store the active bits but generally speaking, VRAM is tons faster than system RAM
System memory completely separate from GPU memory. If your graphics-intensive program requires 4GB video memory, you need a GPU with 4GB RAM for best performance regardless of how much system RAM you have. If your memory-intensive programs do not use the GPU, then you would be ok using the IGP or a very low-end GPU with 1GB RAM or less.