Over a CAT network, probably not for games - you'd need high bandwidth between the main CPU and RAM, and the GPU. However, Thunderbolt is fast enough - though you won't get the most out of higher end graphics cards. External Thunderbolt GPU boxes have been around for around six years (Sony Vaio X), but it's only recently with newer versions of Thunderbolt, and support in Mac OS and from some gaming laptop vendors that the concept is gaining traction.
What you can do over a network is stream video and human input, so the game *runs* on your desktop PC but you play it on your laptop or Nvidia Shield tablet - or run the game in your PlayStation 3 and run it in your Xperia phone or PlayStation TV. I've only tried the latter, and it wasn't perfect with video compression artifacts and dropped frames despite both devices being cable connected to the LAN.
You can share a GPU over a network - or rather a machine containing a GPU - for applications where the GPU is fed some numbers and can return a result when it's good a ready - for example, simulating an explosion, ray tracing an architectural scene or, famously, simulating some protein folding. This requires a piece of client software running in the GPU machine, controlled by the host software in the machine you're working on. Bunkspeed Hypershot, used for rendering product images, works this way. You can the master software on a Windows machine to render a SolidWorks model, and it'll use the GPUs and CPUs on every machine (Windows, Mac, Linux) on your network to render the image more quickly.