No, it's documented, as is tempura. It's like pancakes: you make them before the time of fasting. "The Time of X" in Spanish is "tempora X" and I would bet Portuguese is similar.
There are loads.
https://en.wikipedia.org/wiki/List_of_Japanese_words_of_Port...
It's listed there under False cognates.
> evidence indicates arigatō has a purely Japanese origin
I remain suspicious, though. Maybe what happened was the popularization of an existing Japanese term under the influence of Portuguese Jesuits, since it sounded similar to obrigado?