Read External Button with Arduino Analog Pins

The 2560 can treat one analog pin as ground and measure another relative to that?

You can use a low Vref to measure small voltages on any AVR. Suppose I fed one input to Vref and the other to the analog pin?
LOL, I suggested that to get the difference between light detector reads just days ago.

RTFM? For what voltage is, my manual is a physics book. Depending on the device and environment, device ground may change relative to earth ground or other device grounds wildly.