Since the DSi was first announced, it's been difficult to precisely determine its regional limitations. Rumor spread that everything would be region-locked -- that all Japanese games would be incompatible with an American DSi. That's not true. So far, only DSiWare has been proven region-locked, as a function of region-specific DSi Shops. In addition, Nintendo has said that DSi-exclusive games would be region-locked. But you can still play any normal DS game on any DS system, including the DSi.
NeoGAFfer t3nmilez provides an account that helps clarify the DSi region-locking situation. He imported The Idolm@ster Dearly Stars, which has extra camera features when used in a DSi, and it didn't register in his American DSi; though it worked in an American DS Lite and a Japanese DSi. From this, we can infer that (if his DSi isn't busted) DSi-enhanced games are regionally encoded just like DSi-only games. So if you want to play The Idolm@ster, make sure you have either a Japanese DSi or a DS Lite.