I think I'll still terminate my cable with 4-wire USB and 4-wire ethernet on each end, then I can easily test if it works and if not (hopefully) still use the USB side for 5V power to the Pico!
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Thanks for the advice.
I read this page which gave me hope: http://www.yourcablestore.com/USB-Cable-Length-Limitations-And-How-To-Break-Them_ep_42-1.html#usbethernet but after some more research I think they are referring to active USB-to-Ethernet adapters not simply using ethernet cables with USB terminations!
I think I'll still terminate my cable with 4-wire USB and 4-wire ethernet on each end, then I can easily test if it works and if not (hopefully) still use the USB side for 5V power to the Pico!