Can +5V on an I/O pin destroy the Arduino when it's not powered itself?

Hi, I'm quite new to Arduino, and I want to use a MEGA to control some external circuitry which works at 5V DC and is powered by its own voltage regulator, not from the Arduino. In this setup, it might happen that the external circuit is working and applying +5V to one of the I/O pins, but the Arduino itself has no power supply yet, only a GND connection to the external circuit.
Could this possibly damage the Arduino?

Yes.

Thank you Whandall. Is that your own experience, or can you quote some source that says why?

Shure.

https://www.youtube.com/watch?v=2yFh7Vv0Paw

You mean that the Arduino would be powered through the input protection diode on the input, but the diode would burn if the power consumption got too high?

Yes.

It could probably be avoided by limiting the possible current to those back powered pins,
for instance, with a resistor.