The eGPU dock should have it's own PSU.
But to put things into perspective, eGPU is totally not worth it. You pay a high price for the dock, you'll need to buy the GPU and you need to have a laptop with thunderbolt ports. All this will give you an external GPU with performance that will get nowhere near the performance from an internal GPU.
This was tested long time ago, and if I remember correctly, a laptop with external GTX 1080 was performing about the same as a similar laptop with an internal GTX 1060.