I don't know if code applies to this, but it's not a very good idea. Separate fans, even with their dampers, rarely seal all that well, and if all of them were on at one time, you'd not end up with a large enough set of ductwork or outlet not counting forcing the air you want to extract into those other rooms. You might be in a better situation installing a central in-line fan like one of the FanTec products, and ducting all of them that way. It's not all that hard to install 3 or 4-way switches to control it from multiple areas, but since most people do not run the fan as long as recommended (essentially, they turn it off when they leave the room and it may need to run 20-minutes or more to fully dry out a room after a long-hot shower), adding in a timer or humidity sensor isn't a bad idea, either. You can use proximity sensors, but a fan isn't always needed when someone is in the room(s) involved.
Depending on the distances and elbows involved, even a 4" duct may not be adequate for one fan, let alone more. I'm not a fan of the soffit, either, since the hot, moist air wants to go up, not down, and it can lead to condensation and moisture problems around the vent cap.
