Hi: ( Note that below considers the bivariate case but same type of discussion holds in general for $n > 2$ ).
The impulse response function using the var in differences will not be correct because it will not include the effect of the two levels of the variables being tied together in the long run. It is possible to calculate the IRF using the ECM but the response ( in the bivariate case ) results in both variables moving, rather than the standard impulse response where one moves. I can't do the explanation justice here, even if I had more space, but it is explained very nicely ( albeit briefly. banerjee's textbook is old but nice. johansen and juselius have another and there's another by Lutkepohl ) ) in the document below. So, the short non-detailed answer is that, if you use a var in first differences to generate the IRF when the two series are cointegrated, you won't be getting the correct impulse response. I hope below helps. If it's not detailed enough, check out the textbooks that I mentioned.