Speaking from a computer programming background, MPEG and H.264 encoding do not lend themselves to GPU hardware. The encoding requires a lot of conditional logic and "if statements" where a CPU is superior. The dedicated encoder chip in your camera does not work the same as the GPU in your computer; both are intended for video work, but specialize on different types of tasks. Note a GPU works fine for decoding, which is an easier task.
My personal experience is that few decent GPU encoders exist, and the best ones have slightly higher performance but noticeably poorer quality than CPU encoders. Overall, I cannot recommend OpenCL or CUDA based encoders. But - my experience is from a few years ago. Software may have improved. Side-by-side quality comparison with your particular footage is always best.
Looks like GPUs do have dedicated encoder circuits these days. Support is available in select software on Linux and Windows. See here and here. Adobe Media Encoder is not listed. If it uses OpenCL, then it's using the main part of the GPU and not the encoder circuit, so above comments on quality still stand.