Yes, assuming he got a different power charger to work with the German power grid, it should work just fine. Plenty of people imported the original DS and the DS Lite from Japan before it went on sale in the US. You should be able to buy a "replacement" charger from Nintendo Europe or probably a number of retail stores.
Just tell your friend to be mindful of any import duties that may be assessed. It's not worth being charged with smuggling to save a little money on a game system.
Can a Nintendo DS system bought in America be used in Germany? Will US DS games play on a DS machine used in Germany? Have a friend in Germany that wants to save money by buying the console in America and taking it back to Germany, but not sure it will work on German electrical current. They would want to use games bought here as well as in Germany.