The main question is WHY? I already have a 3570K box running our NAS, plex, Wifi repeater admin, etc, etc, and it would be trivial to put up a web server via python or something.. If I had any need for it.
Sure, a phone could work - but only if you don't already have another server anyway. The downsides of a phone are probably too much of a pain over a cheap $50 used server.
maybe because phones have a battery (built in UPS) so they will keep running if the power goes out. its only useful if you have a router that can be powered by an external battery pack i supoose