Most games can simply "drop frames", when renderer isn't up to speed with engine. The result is minor loss of visual fidelity, which usually isn't too bad, unless FPS are horribly low. Things are more tricky for terminals, because 1) they need to maintain scrollback history 2) their output is more blocky, so "dropping frames" leads to horribly-looking ASCII animations.
There are some terminals, that do start dropping output, when rendered can't keep up. Others (for example, xterm) do refuse to do that by default, because they assume, that underlying program may do better job at handling low framerate, than general-purpose terminal emulator.
Either way, if you want to achieve fluid, visually pleasing rendering, you renderer should be as fast as possible.
Unless you're already using Vulkan/Metal your render thread will most certainly be lockstep with the GPU and that will block your CPU throughput.
You haven't described CPU/GPU independence at all. You're just talking about sacrificing the FPS for CPU perf.