*Update* First off – Why is this important?
Because if you want to catch low light action photography (that includes people interacting naturally indoors) then you will need to test the shutter speed you want to use in that lighting first. The effect is not immediately visible in the viewfinder or back display, but is visible in playback (especially if you flip between photos).
Watch out for artificial lighting when using electronic shutter.
At faster shutter speeds, you may get banding depending on the type of artificial lighting (such as fluorescent). The effect largely disappears around 1/60th in the fluorescent lighting below.
The color between mechanical at 1/250th and electronic at 1/60th is different, too. (I should redo the test both at 1/60th to see if the color changes.)
*Update 12/13/2015* I have recently shot multiple plays and orchestra concerts using the wonderfully silent electronic shutter successfully and have been very happy with the results (I will post about these soon). But it still is a good idea to test the electronic shutter in artificial lighting before committing to shooting the entire event this way.