The hdmi port on your laptop outputs a video signal. There can be nothing on the other end except a display. The video ports on a graphics card also only output a video signal. To use a graphics card on any device, it would need to be connected to pcie. With a low end card, the adapter is going to cost more than the gpu itself. It also gets less performance in most cases so using a low end card makes no sense and would probably be cut down to what the laptop already has. It does need power as does any gpu. The pcie slot itself gives up to 75w and the adapter or card would be connected to a psu.