Not sure what model board you're referring to, or if you're speaking generally. The GPU/PCH isn't "just" responsible for graphics output...it handles so, so, so much more than just rendering video output. I can tell you it would NOT be possible in the sense of literally removing the chip off the board. It's just too vital and the board would never work without the chip in place.
Plus, why not just replace it with a good chip, if you're going to go that far? Just seems inefficient and most likely impossible. All of this assumes you're talking about very, very specifically-damaged GPU/PCH chips, i.e. scenarios where literally all functions of the board work fine except for dedicated-graphics output data signals. Probably not going to see many of those cases. I personally wouldn't recommend wasting your time, unless you're that curious, and you have a ton of free time.
Plus, why not just replace it with a good chip, if you're going to go that far? Just seems inefficient and most likely impossible. All of this assumes you're talking about very, very specifically-damaged GPU/PCH chips, i.e. scenarios where literally all functions of the board work fine except for dedicated-graphics output data signals. Probably not going to see many of those cases. I personally wouldn't recommend wasting your time, unless you're that curious, and you have a ton of free time.