Hmm, I dont think so, the DS is certainly region free, and the DSI will play any region DS games. However from the mymemory website (and others):
"Despite software on the previous DS console being region-free, Nintendo told website Eurogamer that it decided to tie the DSis software to specific geographical regions because the console embeds net communication functionality within itself and Nintendo intends to provide net services specifically tailored for each region.
As a result, if a European gamer buys a DSi in the UK, theyll only be able to play software bought within Europe. The same will be true for North America and Japan."
I would certainly make sure before buying!