Isn't that how Reddit started? Hosted on a laptop. I read that somewhere. They had to keep it around to restart the server every few hours.
I've wondered: if computer makers sold laptops with lights-out-management and detachable displays, would people would repurpose them into makeshift mobile servers and design entire server farms around them, like they have with the Mac Mini. You could have a work/coding environment where if somebody needs to take home the dev server to hack on it overnight, they pull it out of the rack, slap on a display, use it any other laptop, and bring it back in the morning to plug back in.