Does it work like this?

Solution
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.
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.
 
Solution
All ports that can be used for egpus, mpcie, expresscard, m.2, and tb, all cannot supply 75w so the egpu has an external psu as well.

https://www.techspot.com/review/1575-external-gpu-gtx-1080-8th-gen-ultraportables/ This shows the performance of a 1080 egpu was closer to the 1070 but they are using a U cpu which was shown to be causing some bottlenecking. There are cases when egpus are worth it. When the laptop has a decent enough cpu but just an igpu, a mid range egpu can make unplayable games be played on medium even when using mpcie. That could cut the extra cost of an adapter down to $10 and the psu and gpu can always be re-used. Of course 2.0 x1 is more of a bottleneck but at least they're not burning $200+ on an adapter.
 
If it's a good idea or not, is another topic. What I'm assuming you are asking is if the external pcie slot will power a graphics card that doesnt require supplementary power connectors (example gtx1030). I would assume it does. I think if you gave the egpu dock and port you are using someone could give you a better idea. I do believe a regular pcie slot supplies up to 75w. And would have to assume an enclosure built for it must supply it that much power. Since a graphics card with extra power connectors, I have to guess uses that 75w in addition to them. I would also assume something like a thunderbolt 3 port can supply the pcie board the 75w. But maybe the external power supply also supplies the external pcie slot with power. (I'm just an amateur with no experience in external GPU. Most my assumptions are just based on semi educated guessing. So I didnt want to sound definite)
 


And if you're going to use a GPU that can be run off the PCIe connection, it is pretty low powered (1030) and not really worth the effort of the eGPU concept.




No they don't.
There are "eGPU" things you buy which is simply the cable. No power at all.
Until we know exactly what the OP has or is considering....its all just speculation
 
The commercial egpu enclosures do come with a psu, actually a power brick for most of them. The adapters you can buy separately will not work without that either. Expresscard ~5w, mpcie ~10w, m.2 25w, tb depends on version but usb c is 100w. Besides tb3, they can power the adapter but not the gpus connected to them.