In general copper traces do add negligble stiffness. However, when you have close to 100% coverage on a layer (such as the ground plane, and occasionally other planes), then it matters by perhaps as much as a factor of two or more if the planes are 2 oz thick (.00270 inches).
What are the implications of analyzing a PCB that is less stiff than reality? Well, your results for bending would be conservative. Your natural frequencies would be a less than they are in reality and as long as your consistent in multi-PCB systems, you'd still pick up on if the boards will be resonanting together. The calculated PCB deflections due to vibration would again be conservative. However, sometimes this is a problem if you are failing under conservative assumptions. Neglecting copper cannot be done if the PCB laminate material has a CTE that varies greatly from the copper. I should add the method of copper foil attachment matters as well. You can find that information out from the lamiante vendor, so far I believe electrodeposited copper can have the greatest resistance to interlaminar stresses. Interlaminar stresses around vias and fastener holes can get quite high. Stresses due to bending and thermal expansion can rip a board apart.
It seems the easiest way to model a PCB is using a finite element code. ANSYS for example makes it fairly easy to model a simplifed lamiante of copper/laminate/copper. I only count the copper planes with 85+% coverage. I've just begun working with PCBs this way. However, I anticipate that in large models dealing with 10+ PCB boards, the run time increase will not be acceptable. So what I'll probably do is try to extract a stress/strain curve from a detailed modeled PCB and use that as the isotropic young's modulus.
