I was actually wondering this myself the other day. Since I have internet access right now and because you asked, I poked around for info.
Nintendo has reported that the DSi uses region locking for DSi-specific software, since the handheld provides Internet services tailored individually for each region, and uses rating-based parental controls which differ by country. However, elements such as Internet browsing, photo sharing, and Nintendo DS software are region-free.
You will indeed be able to play the Japanese version of HG on your DSi. :)