Yes drinking bad coconut water can make you sick.
However the worst that will happen if you did drink bad coconut water is that you get a stomach ache, stomach cramping, diarrhea, vomiting and nausea.
You're unlikely to get severely ill from drinking bad or spoiled coconut water but if the coconut water is bad enough it will have a disgusting taste to it or a bad or disgusting smell to it as well.
If the coconut water has gone bad or smells bad or tastes bad then dump the bad coconut water out to avoid getting sick.
As long as it smells good and tastes good then even if the coconut water has expired it's likely still safe to drink.
But if in doubt about the coconut water being good or bad it's best to just dump it out and not risk getting sick from it.