this thread is ancient, but yes, itll work:
Aside from region locks, the 3DS are identical and take in the same voltage. The power adapters taking in the AC however are not identical!
Common Regions:
China, USA and Canada = 100-130V AC @ 60Hz
EU, Russia and Australia = 220-250V AC @ 50Hz
Japan = 100V @ 50 or 60Hz (depending on region)
Overall, you can safely use devices from Europe in for example Australia, however, they use different plugs, so you'd need a simple adapter.
If you go on a journey from Europe to the US for example, a simple adapter will not suffice. You need a current and frequency converter, otherwise your power supply and whatever is connected might be toasted, unless they accept 100-240V @ 50-60Hz.
Same rule the other way round, of course!
As for the different plugs and sockets I've mentioned:
There are basically four big types around the world:
The European plug, the US/Canada, the UK plug and finally the Australian plug
An extensive list of currents, plugs and countries can be found here:
https://en.wikipedia.org/wiki/Mains_electricity_by_country
Or just take a look at this beautiful graphic:
http://worldwanders.com/tcomp/spread of plugs around the world.gif
For all those that see this as too technical and all:
USB ports are the same around the world, so just get a USB cable for 1.45USD/1€ with free shipping instead:
https://www.fasttech.com/products/0/10000045/1008900-usb-charging-cable-for-nintendo-3ds
P.S. EU Standard is 230V, however a deviation of up to 10% is allowed: 207-253V