Desktop GPUs on Laptops?

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I'd say that it's probably rather optimistic on the G6. As far as I can see it's only got a PCIe x1 slot which the wireless card is in (as @Foochow said) which will severely limit the performance of any graphics card you may decide to plug in there (graphics cards usually run on x8/x16-speed slots), provided that it even works in the first place, of course: I can't see any previous attempts at this for the G6 anywhere online, unfortunately.

Probably not the answer you wanted, I know, but as mentioned above, it's unfortunately more of a workaround than a replacement; it comes with a whole lot of downsides and you'll probably still be limited by the performance of the CPU on the G6 in most games even if the GPU can keep up.

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