The 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. If potential output-growth rates differ, actual growth rates may differ as well. That does not necessarily indicate any lack of real convergence.
In the longer run, stability must be built upon economic integration, which brings about structural convergence. An extensive body of theory has evolved on the characteristics of optimum currency areas. The most important feature is that prices and wages must be able to adjust flexibly. The mobility of goods, labor and capital will ensure market integration.