Okay, so the summation of the nights speculation:
1. Building an ESP8266 or Arduino based PC would probably be more complicated than worthwhile, mostly because of the work that would need to be done to enable video output.
2. SymbOS exists and supports Amstrad CPC 464, 664, 6128, 464+, 6128+ and is just really neat looking.
3. ESP8266 based serial wifi modems for vintage computers exist and are pretty neat and a good idea.
(cont.)