Not neccessarily. If the material has a density less than 1 (like balsa), you are correct. Otherwise it will sink. The example was meant to illustrate that shape affects volume. If the box is made of steel (like a ship) and you crush it, it will sink.

Maybe. It will only sink if the density is greater than 1 even if it's full of water (the material still has some volume even if the box/airplane is full of water). It's the total density of the object, not any one material that composes the object that will determine how it floats. If, when filled with water, there is still enough displaced volume to keep the overall density less than 1, then the object will float. That's why I suggested plastic air-filled bags in open spaces of the plane. The fuse and wings are full of air anyway, all you add weight-wise is the the weight of a plastic bag to seal that volume of air in place.

Yeah, kinda figured that would be tough to talk someone into.

But, you can figure out some estimate of buoyancy without doing that. Let's say you had a volume that looked like a box 20cm on a side. That's about 7.8 inches on a side. A typical .40 size plane probably has at least that much volume. You could just do some basic estimates treating the fuselage as a box and the wing as a box to check.

A cube that size has a volume of 20x20x20 or 8000cc. 1 cc = 1 ml. So an 8000cc volume would displace 8000ml * 1g/ml = 8000grams of water. 8000g/ (454 g/lb) = 17.6 lbs. So if the weight of the plane is less than 17.6lbs it has a density less than 1 and will float. It probably wouldn't fly though.

A plane that size is hopefully more in the 8 pound range. That weight would only need a total volume of about 3600ml (or cc) to float. That's a cube about 15cm or 6" on each side.

The point is that if you know how much volume is needed to support the weight of the plane, you just have to make sure that you have at least that much sealed volume (without adding additional weight) in order to keep the overall density less than 1. You don't need to know the actual total volume, you just need to know it's more than the minimum required.

I think we agree on most everything as well.
The shape doesn't affect bouyancy but it does affect stability and to some extent efficiency. Like bruce88123 pointed out, barges are often flat bottomed. Supertankers don't have much of a V either. The shape does affect things like stability with increasing load (like your example), drag due to frontal area, and the amount of surface area (material) per unit of volume. But, the shape doesn't directly affect the density (and therefore buoyancy), that's strictly a function of mass and volume like you pointed out in an earlier post. You can use most any shape to make any volume you like.

Ditto on all counts. Usually this kind of discussion just devolves into a slander-fest. It's nice to have the occasional civilized exchange on an internet forum just to prove it's possible.