That's possible, but would be tricky to implement... however most graphics setup and animation code runs super quickly on GPU, as that kind of (math heavy + super parallel) code is much better suited for the GPU than the CPU. On GPU side you can use GPU generated structures (such as the depth buffer) to do more precise culling, freeing more GPU cycles than the culling stages cost. It might sound a bit strange, but sometimes moving processing to GPU saves BOTH CPU and GPU cycles.
That's definitely possible. Alternatively you could output always at 1080p and vary the pixel quality (use some sort of iterative refinement technology and give it always the same time). For example this OpenGL extension (timeAMD) can be used to do GPU side timing:
https://www.opengl.org/registry/specs/AMD/gcn_shader.txt.
I always choose locked 60 fps over 1080p. With Trials Fusion we unfortunately had to render at 900p on Xbox One. But it was a "launch window" game and we had to support DX10 PCs and Xbox 360 using the same code base, meaning that it was impossible for us to implement a brand new fully GPU compute based engine for the game. Xbox 360 was a high priority for us since we had such a large fan base on that console.
It's nice to see that people are moving to the next gen consoles faster than anyone expected. It took more than 3 years until PS3 games could compete with PS2 games in sales. Fast next gen adaptation will definitely allow the developers to start focusing on next generation sooner, and I am sure it will improve the quality of the game visuals.
You don't always need to sacrifice pixel quality to increase your output resolution. I'd say that 720p image reconstructed to 1080p (using for example a 1080p depth buffer) would look better than 900p in most cases (as the edge quality would be equal to 1080p). Obviously to reach a perfect result everywhere you'd need more input data (than just a depth buffer) at 1080p and you wouldn't want to lock in the material processing quality to some fixed resolution (like 720p). You'd want to analyze the screen and determine the sample locations dynamically. Definitely you can do more with less, if you are clever. Sometimes you can have both: good pixel quality (where it matters) and good resolution (where it matters).