If you’ve got some natural resource within your borders, one that lots of people want to buy, then you end up getting lots of foreign money being changed into your local currency as people buy that resource. That drives your exchange rate up and thus strangles everything except that natural resource.
That isn’t the resource curse, that’s Dutch Disease, so named because after the Dutch discovered Gas all their other businesses became uncompetitive. The resource curse is more complex than that.
Currency appreciation may be bad for producing and exporting things, but it is very good for consuming and importing things. Both of these things are good things to do, it is all about degree. To call either circumstance a curse is a misnomer. Consuming things is the point of economics, were it not why invest in a gamble to consume more in the future?
No, I think currency appreciation is a significantly smaller part of the resource curse than is the fact that the presence of valuable resources make it more profitable for elites of one shade or another to seize political and economic control of a country’s institutions.
Acemoglu and Robinson have a blog all about this.
Having an overvalued currency might depress output in a few exporting sectors a bit, having competing meglomaniacs try to take over your country will crush economic activity everywhere.
The most important thing a developing country can do is to enforce fair rules in a predictable way, natural resources and the super profits available from their sale, make it incredibly easy for one group or another to evade, subvert or supplant the law.