This is somewhat anecdotal so take it with a grain of salt. I think working at a Japanese firm would be a nightmare. I'm an architect in the US and went though the studio system in university and understand that culture. I also lived in Tokyo for two years working -- not in architecture, but I did an internship at RTKL's Tokyo office, which is now closed.
I would never, ever, work for a Japanese company. If I could pick any city in the world to live in it would be Tokyo, but the ridiculous attitude Japanese have toward work is enough to offset all of the good things about living there. This is not based on my personal experience, this is based on knowing the experiences of many people at many different companies. I would work for a foreign company based in Japan, but definitely not a traditional Japanese company. Even if they have progressive designs, you'll find that the architecture and construction industry in Japan is very traditional and conservative . A typical Japanese company is extremely hierarchical, and values effort over skill especially for low level employees. That means that you better put in more face time than everyone equal to or above you or you will be looked at as a slacker. Even if you finish your work it doesn't matter, gotta stick around and look busy. As a foreigner you will get a pass on this to a certain degree, but I'm not sure how it would work at an architecture firm with a revolving desks for foreigners. But I also think that situation would make them less interested in investing in training or educating you.
Combine that attitude with architecture studio values and I imagine it would be a real match made in hell.
I doubt you would get to actually experience Japan since you're going to be locked in a room working day and night. And why are you taking an unpaid internship? The economy is booming now. I mean, I get that it's at a firm you admire, but that doesn't mean you're going to automatically learn a lot or be mentored in any way, you may just be used as labor. What country do you plan on practicing in? Some of what you learn to do in Japan is not going to be usable in other countries.
It'd probably be better to get a PAID internship at a firm near you with a reputation for mentoring interns. Then take that money and take a trip to Japan and see the country, travel, understand the urban fabric, go visit and touch some of the buildings by Japanese designers you love, maybe set up some coffee or lunches with architects and designers -they don't have to be the head of a firm or even architects to learn a lot from them.
All that being said, the bottom line is that if you think this is a truly golden opportunity and it's something you would look back on and wonder "what if" if you didn't do it, then go for it. I don't know exactly what your goals are, but just remember that there are usually many ways to reach a goal.