Can I power a 2560 with a 5v 2.5 wall wart PS?

The only difference between the USB socket and the 5volt pin is a 500mA polyfuse inline with the USB socket.

Adding a diode would lower the external 5volt supply with a diode drop (0.4-0.7volt).
If you're careful not to reverse polarity, then don't use a diode.

The only difference between V-in and the DC socket is a diode inline with the DC socket.
Not a problem here to drop 0.7volt from a still unregulated voltage.
6volt on V-in (6.7volt on the DC socket) is the absolute minimum for the regulator to make a stable 5volt.
Leo..