Not coming on this forum as an expert here (hence why I'm looking at this forum), but with ur question..,
The 5600g is a graphics enabled CPU yeah?
I'm pretty sure the answer to ur question is a flat no.
The 5600g may even require u use its physical Mobo output to do anything, so you're talking about swapping connections.
And then 2ndly, there'd be absolutely no technical advantage to do so either. Ur 6600XT is superior for graphics in every way. Ur CPU graphics is redundant hardware sadly (best advantage is as a good back up to keep ur PC running if ur GPU card fails).
It sounds like ur thinking that, if u use the CPU graphics to take the load off the GPU card, things will be faster.
I'm pretty sure graphics doesn't work like that unfortunately though. Firstly, ur desktop display requires hardly any GPU resources, so little would be improved anyways, but more technically, the way graphics is displayed.
All a game is within say Windows, is just another window (usually full screened).
The system is using the GPU to display output for ur physical monitor screen, not individual app windows within ur operating system.
In the case of the multi-gpu card setups (SLI/Crossfire etc..), the multiple cards are being used simultaneously to draw the one full output to the monitor, again, not for individual applications
