DaveO:
is it reasonable to assume that, once any load, no matter how large or small ( like the brand new un-used Mega ) is connected, the transformer or circuitry of the power supply could start it's gradual loss ?
Yes.
Sort of.
A very light load might not cause the problem. eg. A single Arduino on a 5A supply isn't going to draw much. The only way to find out is to try it.
Me? I'd disconnect the power supply and apply a bigger load, see what happens. Draw a couple of amps from it and see how it holds up. Have you got some high-power LEDs or anything like that? A bunch of high-wattage resistors?