I really don't know if the fermentation process modifies the goitrogens, but I would say it's irrelevant (must learn how to spell that word...). They also say that cooking destroys or lessens the goitrogenic effect, but believe me, if you are really sensitive to them, it doesn't help at all!
So, by that you can guess that what informs my advice is experience. When my thyroid was working - now it's dead from Hashi's - I couldn't eat strawberries, walnuts, pears or maize. And it didn't matter if they were cooked or whatever. I even had to give up walnut and coffee cake! Can you imagine? lol
So, yes, the adverse effect is very immediate - within an hour or so, usually. But it varies from person to person. I have also done a lot of reading on the subject and discussed it with people and the general opinion seems to correspond with my experience.
It was quite frightening before I was diagnosed and before learning about goitrogens. I just couldn't understand why strawberries made me so ill. I didn't break out in a rash or anything, or start sneezing as I did with my other allergies (not food related) so I didn't think it could be an allergy. And lo and behold, it wasn't! But I find it's difficult to explain to other people why I couldn't eat certain things, they didn't understand, so I just fell back on calling them allergies... Ho hum.
Anyway, if sauerkraut is making you feel good, then carry on with it! I find that interesting because I've eaten plenty of sauerkraut in my time and didn't feel any beneficial effect. But it's interesting to know that it can be benificial for some people. Enjoy! I say. lol