Can electronics be damaged by under-currenting it?
Conceivably yes. Limiting the current means that the circuit will attempt to draw the current but the supply limiter will reduce its output voltage in order to balance the higher demand of current. 

We are back to a lower voltage or under-voltage scenario and I can envisage a situation where a weakly designed circuit will potentially be damaged.

A buck convertor may be specified to run from (say) 20V. It's output may be 5V to a load that might be 1A (5 watts to the load). Ignoring losses, it will take 0.25V from the 20V supply in order to do so and it may be fused for say 0.5A. An associated part of the whole circuit may nominally require 2A and if you current limited the supply to 1.5A and the voltage dropped to (say) 6V the buck convertor could be taking 0.833A.

It's a tortuous example but it could happen and the fuse blows. Maybe there wasn't a fuse - the buck convertor transistor will get too hot and if it is a BJT type it will destroy itself.