Vaughn,
• The resonance of a wall cavity has nothing to do with room modes. (I wasn't sure if that was a conclusion or not - thought I make it clear just to be safe.)
• The construction of a room will affect its resonant frequencies. The equation used to calculate room modes (referenced in Everest above) assumes completely rigid boundaries. This is difficult to achieve in reality. Several feet of solid concrete comes close, but still isn't perfect. An assumption of rigidity is an assumption of zero damping. A more complete version of the above referenced equation would include (among other things) a damping factor. A single layer of drywall over studs (no insulation) has damping associated with it. Insulating the wall restricting drywall's ability to damp. Dead-sheet (like mass-loaded vinyl, or visco-elastic compounds) or even more drywall will also decrease damping. The less damping there is, the closer the measured natural frequencies will be to the predictions using the equation referenced above.
• Adding fuzz or foam to a wall increases damping in the room and, therefore, also changes the room's resonant frequencies.
• The differences between the frequencies calculated and those measured - regardless of damping - are not usually significant, with one exception: If there are plans to build Helmholtz (resonant, tuned) absorbers to address specific low frequency problems, it can only be done in situ. I.e., "off-the-shelf" Helmholtz absorbers can never be an economical reality since it's a complete crap shoot whether the center frequency of the device will be anywhere near the problematic resonant frequency. Tuned devices can work extremely well, but they must be built, tweaked, and fine-tuned in the room to address the room's specific problem(s).
• All of this is moot if the ultimate solution being planned is broadband low frequency absorption. When using this "brute-force" approach, most problems down to a certain frequency will be more or less attenuated equally.