Do you need to power down outputs when connecting strings?Can you destroy a pixel chip by plugging in or unplugging a light string on a running system?
Yes you absolutely can, I've done it a couple of time before I learnt. Just thought I had failing pixels until I was enlightened, haven't had one since. (for that reason anyway)
On our commercial gear, in the instruction manual it says
" Do not connect or disconnect any cables from the device while it is energised "
The reasons for this are not just about destroying pixels, its about safety as well. The most likely time for something to go wrong is when you plug something in our disconnect it. If theres a bad mains connection or a dodgy earth, it might really bite you.
From a pixels perspective, I know you can destroy WS2801's, if you disconnect the Earth before the CLK, DATA and +V, and the driver line doesn't have any resistors in series. Current can find a path through the IC, and seing these paths where only designed for logic levels, they don't do so well if you try to pass a few amps.
Other pixel driver ic's have other fault modes.
It is likely that for the main you will get away with multiple live connect/disconnects, but one day it might just break something.