Yep. The only downside is that if a policeman is in a bad mood you may get stopped and checked to make sure you aren't a thief. Only heard of it happening to foreigners (not myself though) but it's a good idea to keep a card in your wallet or a photo of your registration (which is actually a really good idea for anyone traveling/living abroad: if you can keep them in a safe/encrypted place, carrying a photo of your passport, gaijin card, etc. is a pretty good idea in case you put on the wrong pants one day).