It would work, but not like I think you think it would work. Rapid Shot simply adds 1 extra attack. Period. It doesn't matter how many weapons you are wielding or what other attacks you are making in a round, Rapid Shot ONLY adds one extra attack. Kinda like Haste. Or Whirling Frenzy. Or Flurry (well, until Greater Flurry).
So, if you got 4 attacks with your main hand, and 4 attacks with your offhand, you would have 9 attacks with Rapid Shot. If you also had Haste, you would have 10 attacks, and if you added in Whirling Frenzy, you'd have 11.
I built a build a while back that used Master Thrower, TWFing, Rapid Shot, and Dancing Mongoose to get like, 22 dagger toss attacks in a round, each with +9d6 fire damage from Dragonfire Inspiration. It was silly, but completely rules legal.