Can't say for sure, it depends of the exact schematic. Many schematics have a series regulator transistor, like the one you attached. I imagine if you push too much current, the BE of transistor(s) might become reversed polarized. Usually Vbe in reverse is very small, only 5-10V. So if the output of the PS becomes -10V instead of +10V, then it might damage the transistors, though that would probably need a few hundreds of Ma to happen, but I'm not very sure, I didn't try.
A small current from the outside should be safe, because it happens all the time when, for example you set the voltage 10V, the capacitors of your circuit charges at 10V, then you set the voltage to 5V. After this, the output capacitors will push their accumulated energy into the power supply, until their voltage drop from 10 to 5V. That wouldn't damage any power supply.
The problem is when you connect a powerful battery, for example you charge a car battery and an unexpected mains power surge occurs. In this case, the car battery will start to discharge through teh PS, which might damage the reversed polarized transistors. Because of this, in the user manual it might be mandated to always charge batteries through a series diode.