Could a "Japanese-style strike" work as it's supposed to? Under what conditions? This is an urban legend, mostly believed in Spain and some countries in South America.

The legend is based on the premise that their way to make a strike would be to work much more than usual in some goods production, this would cause prices to be lower due to increased supply in the presence of constant demand, so the owners of the business would end up losing money (or making less money) because of that, due to usually planning goods production with the "just in time" method. In addition they would have to pay employees for that day of work and storage costs for excess production, which might be high.

I don't think this would work for every case, but maybe for some it would be plausible.

Would such a type of strike be able to do something similar for at least some cases? If so, in which ones?

We can consider that legally speaking there's no limit to no the number of goods that can be produced.
Without the cooperation of at least mid-level management I dont think that such an approach can work even in theory. Management sets the quantity of ressources and intermediate goods the striking employees have at their disposal to use as inputs. 

The theory is inconsistent in the sense that on the one hand it relies on assuming JIT (for its lack of large storage facilities for final products) to obtain the dumping of a large quantity of output on the market. On the other hand "no limit to no the number of goods that can be produced" implies either large storage facilities for inputs or that the company striking is Bertrand's water well.