Depends on where and how you plug it in. If you just plug it in to a leftover molex then nothing will happen to your system. If you plan to connect the fan the a MB fan connector I woul not do it while the comp is on.
BTW what is the problem with shutting the comp down the 20 sec. it takes to plug in a fan?? No matter how you twist and turn it, it's always best to turn of the PC when starting to stick your fingers into it
As long as you have a stable PSU, your not going to have any problems plugging in to the molex while running. I do it all the time.
I also have plugged in to the mobo connector while running a couple times. I had no preblem with it, but It's really not a good practice.