There could be an extremely slight possibility we could get showered with some debris on exit. The breakup would have to be violent enough that pieces would be launched with enough velocity (thousands of mile per hour) on a highly unlikely earth intercepting trajectory, to cover about 30 million miles in about 30 days or so. Those would be the most dangerous though. Individual debris would be much larger than anything we would likely encounter in the tail debris (unless there are trailing elements) and moving much faster, about 250,000 mph! :-)
Isn’t ISON on an elliptical orbit, and due to enter the Sun’s gravitational field, causing it to whip back out into space in roughly the same direction it came from? If so, wouldn’t this gravitational whip action be unpredictable with a comet that was in pieces?