I would have to say that under those circumstances, yes it may be worth it to send the Japanese Navy towards Europe. It would be well worth it to sink as many transports as possible in the European theater.
The only thing is, it takes several turns to sail a fleet up along africa, through the Med, and then engage the enemy in a preferable battle. It seems like when two fleets are inches from battle, most often a game of cat and mouse develops where the attacker is forced into a battle they might not want.
But if you have 2 IC’s pumping land units and a homeland fleet also channeling troops while protecting from bombardments, it may be valuable to send the fleet over. Sometimes it seems like there is really no alternative choice of what to do with the Japanese navy.