It depends on which rods you buy and where you buy them. Low end Japanese rods don't have any warranties. More expensive rods do. If you buy the rod from Finesse-Fishing.com the Japanese warranty is honored. You have to have the warranty card, but you don't have to fill it out. You have to return the part to Finesse-Fishing (in the US), not to Japan. Finesse-Fishing sends the part and the warranty card to Japan. If Finesse-Fishing has the same rod in stock, you don't even have to wait for the part to come back from Japan - it is taken from a rod in inventory.
However, all the Japanese rod warranties I've seen are one year, one use, one part - meaning you can only use the warranty once, to replace one part, within one year of purchase. There is a warranty processing fee that varies depending on the rod, but is generally in the $20-60 range, plus the cost to ship a replacement part to you (from the US, not from Japan).
Please note that this service is offered only for rods purchased from Finesse-Fishing.com