This paper addresses the following question. Could the BRICS countries have formed a sustainable economic and monetary union (EMU) if they had decided to do so in the early 2000s? Our sustainability criterion is that the macroeconomic imbalances of the countries should not deviate too far from each other. We consider a convergence-based approach to quantify such a situation. We investigate a scenario where each country's bilateral nominal exchange rate is defined in relation to a central rate defined by considering a basket of the various BRICS national currencies. We find that the group would not have formed a sustainable EMU from the late 2000s onwards. We conclude that this makes the project of de-dollarizing their respective economies not necessarily viable, unless the group choose a proper exchange rate regime.