GPUs usually run on big command buffers that are generated in a streaming fashion and then submitted at specific points, so it's theoretically possible that a game could hit 60fps this way. You'd just be eating extra latency between command buffer submission and actual rendering.
Not so sure about no-go. The amount of GPU latency in modern AAA titles already approaches 20+ms in the most egregious cases.
Unless there is a need to evict all gpu memory on every frame, I think it is feasible to game on GPUs that live across a very fast LAN.
Fast ethernet is getting cheaper than ever - you can easily get 10gb on consumer gear or even 20 and used hardware on I believe 40 or maybe 100 is getting pretty affordable.
In my experience 40G gear can often be had for cheaper than 10G. I have a pair of Mellanox 40G Infiniband cards that cost me about $20 each on ebay and could be turned in to Ethernet cards with a few commands.
Output screencast could be encoded right in GPU pipeline