No, because both areas were filled with minor principalities governed by leaders who guarded their power quite jealously and would not be willing to give it up to a greater nation without a fight. In addition, both Germany and Italy were the scene of major imperialist fights for territory-if the HRE breaks down, then it successor states in Austria and Spain as well as France, Sweden, and Poland go for the German territories. Austria, Spain, France, the Pope, and even the Ottomans will all go for the Italian territories.
In addition, any kind of German unification at this time is highly unlikely due to the religious wars caused by the Reformation and Counter-Reformation.
As an aside, I'm not sure if the Italian territories were considered part of the HRE. Yes, the Holy Roman EmperOR had holdings in Italy, but I believe these holdings were legally and politically distinct from the German states.