I hear this argument a lot, but I don’t quite understand it.
Let’s start with a contrast, namely that Ecuador, El Salvador and Panama all use the U.S. dollar. It is unlikely that lowers the value of the dollar and since it boosts the demand for currency it may even strengthen the dollar a bit, though of course there is a Fed offset on the currency supply side. The U.S. may have a partial geopolitical commitment to these countries, but it has to do with location, the Monroe Doctrine, and the drug war, not with their currency choice per se.
So why does it lower the value of the euro to have Greece use the currency? The simplest reason is that Greek participation, and involvement of the other periphery countries, creates a real chance that the eurozone will blow up, partially or fully. (El Salvador does not pose a comparable threat to the dollar.) Fair enough. But then it cannot be argued that the lower currency value means Germany can/will stop such a blow up. In equilibrium those are inconsistent conjectures. For the blow up option to lower the value of the euro, the blow up option must be real and if that is not a real risk now when is it supposed to be a real risk?
Another option is to claim that the the participation of the periphery countries in the eurozone raises the expected rate of price inflation in the eurozone. First, it’s not clear this is true and it has not been true so far. Second, it is not obvious why the euro should become weaker before that higher inflation arrives. Third, if German export prices are equally flexible it doesn’t give us a weaker real exchange rate for Germany, which was the original supposed benefit. Fourth, if German export prices are not flexible we have an overshooting model, which a) implies the low real exchange rate for Germany goes away over time, and b) implies that far more real exchange rate volatility is predictable than is actually the case.
A related question is whether solving the eurozone crisis, for ever and ever, with a neat nifty eurobond (or whatever ha-ha) also would remove Germany’s supposed real exchange rate advantage.
My analysis has not exhausted the options but perhaps you see the problem. I have not yet heard a coherent version of the argument. The simplest answer, and the answer most likely to be correct, is that the euro is lower in value, to the benefit of German exporters, but only because there is very real chance of a crack-up, and this is a reason why a crack-up might happen, not a reason why a crack-up will not happen.
Ultimately, the conjectures have to add up.