Sadly no, your GPU doesn't use that much RAM. Going to 8 gigs of RAM will not speed up your performance.
The GPU is a graphics processor, and currently you will probably have heard of "dedicated" graphics and "integrated" graphics processors.
The main difference between the 2 is that dedicated GPU's have their own on-board Video memory and thus don't have to share the same memory pipeline as normal system RAM. Thus they usually outperform integrated cards by a mile. Dedicated GPU's usually also have a much larger number of texture units and cores, so they also pack a lot more processing grunt.
Integrated GPU's on the other hand lack their own onboard memory and have to share resources with the processor. This means the memory pipeline has to serve both the GPU and the CPU.
On top of that it also reduces the amount of memory your CPU can use because some of it is being used to store textures etc.
Integrated GPU's are also much, much weaker than dedicated GPU's because they don't pack enough texture units / ROP's.
Past 4 gigs of RAM, anything you add to it doesn't change the fact that it is still an integrated GPU.
Adding a bigger fuel tank to a slow car won't make it win any races.
The only way to speed it up is upgrade it's engine.
I don't recommend wasting your money on extra RAM. Go get yourself a dedicated card like a Radeon 4670 or even a Radeon 4850.