The Governing Council of the European Central Bank designs monetary policy appropriate to the euro area as a whole. A country whose business cycle gets grossly out of step might suffer if it is subject to a monetary policy that is inappropriate to its national economy.
However, marching in absolute lockstep is not necessary, as can be seen in the USA, where certain regions grow faster than others. Growth rates of states and regions within a currency union may differ to some degree. It is the size of the gap between actual and potential growth rates which matters.