Hi Jon,
just for the record, x264 is the software H.264 encoder, that doesn’t make use of the GPU, while you want to leverage the hardware encoding made available by the graphics card, namely NVENC. Hardware encoding support is not available in virtual desktop sessions when X11 vector graphics mode is enabled, as explained here. You can try to disable X11 vector graphics, so that hardware encoding will be used, and compare the results. It will mostly depend on the applications used.
The graphics card is also used to accelerate the applications running in the virtual desktop, by means of VirtualGL support (https://knowledgebase.nomachine.com/AR05P00982). This would only be useful if you run applications that use OpenGL for rendering.