Pretty much. The actual weight-loading on a wheel is minimal compared to spoke-tension. Basically with 200lbs of tension on each spoke, the greatest load on them is trying to compress the rim inwards while the rim is fighting back and trying to stay its original size. The hub-flange is always being yanked by the spokes. When you add weight to the axle, you relieve some of this 200lbs on the 3-4 spokes at the bottom which are being pressed upwards.

So a 400lb gorilla will add 200lbs to each wheel and relieve tension on 4-spokes at the bottom by 50-lbs each, or 25% of their total tension. This compresses the rim in that spot and it tries to expand all the way around the upper parts. This adds 200lbs of load to all the other spokes, or about 6-lbs each. A wheel is basically an inside-out suspension bridge or like a balloon. Push down on a balloon and you'll see that the areas not being pressed expands evenly. Overall total tension on the skin of the balloon remains the same, some areas facing external loads have tension relieved, and that force is evenly spread and added to the remaining unloaded skin.

The biggest factor in determining lateral-stiffness is then the width of the flanges and to a lesser extent, the numbers of spokes. If you look at the test-data table above, you'll see that there's two radial-wheels with the same specs. The only difference is that one has the spokes coming from the inside of the flange and the other on the outside. The wheel with the spokes on teh outside (wider spacing) is measurably stiffer in the lateral direction. Imagine if you had a hub so wide that the spokes met the rim at a 45-degree angle, that would make for a super-stiff wheel laterally.