No, you can definitely run a Vive off an eGPU but your success will depend entirely on the system you're plugging the eGPU in and the GPU you're trying to drive (as different eGPU lines will have different compatibility matrix due to GPU architecture differences). OP started a dupe thread in which they shared their laptop specs - they're working with a very entry level HP gaming laptop that's underpowered to the point where it doesn't even support HP's Omen Accelerator eGPU.
In almost all cases, you'll see better perf and better cost effectiveness to run VR native hardware. Frankly speaking, adding an eGPU fundamentally adds another device to the processing and signal chain that could create troubleshooting issues which can ruin UX and waste time.
I've used a Razer Core X numerous times before - it works but it wasn't a crazy perf win, especially considering the price tag.
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In almost all cases, you'll see better perf and better cost effectiveness to run VR native hardware.
I agree, although thats not really the point, nor was it the (original) question.
I do have a small update. I tried a Razer Core X with a GTX 1070 and got an average of 150 FPS on VRMark Orange Room (109 FPS is the target FPS for Vive/Rift recommended spec PC). This means that (at least for my CPU, which is decent with a ~11000 score on PassMark) an eGPU is more than capable of running a Vive.
I plan to try a M.2 M Key adapter soon (which apparently can get much closer to "native" GPU speeds), so maybe I can squeeze a little bit more out of this card as a DIY eGPU.