I am currently growing out a Japanese straightener also. I had a total of 5 of them over the course of a year and a half, the last four concentrating on the roots only, of course.
The damage for me wasn't immediate, but as the straightened parts got longer, they got weaker and weaker, more than they would have without the process. My hair is pretty long, though, between BSL and waist, and resilient so I could handle the breakage at the bottom.
Now, to agree with the previous poster, OMG, the roots are SOOOOOOOOOOOOOOOO annoying when they are coming in. Seriously, I would drive my husband insane in between touchups. It looked strange and you had to do so much to deal with it: pull your hair back, blow dry, etc...that it defeated the purpose of having your hair straightened in the first place.
And, depending on your hair texture and who does the process, your hair can look...unnatural. Mine looked good because I babied it to death with DT, oilings, etc...way too much time on my hair but there are a ton of people who came into the salon whose hair looked...like a really bad wig or something. In other words, it is not as carefree as I thought it would be!