That's the key question: at what point does the bracing/cabinet no longer contribute towards an audible improvement?
If the cabinet resonances are below the masked detection threshold, then you are over-engineering the speaker. Remember that for resonances at higher-medium Q-values, the level of the cabinet resonances must be almost as high as the output of the transducers to be audible.
So to answer the question, you need to apply a psychoacoustic model to the FEA output of the speaker cabinet to determine if the bracing produces audible changes.
There is an intermediate step required, which would be to do a coupled field analysis of the fluid-structure interaction to calculate the response of the air to the cabinet movement. From this analysis, the acoustic output across the frequency band of concern could be calculated. In general, because sound pressure amplitude is a function volumetric change, larger panel movements will
always produce more sound. The amount of sound depends on the amount of coupling of movement between the panel and the surrounding air, which can be described as radiation efficiency.
Whether or not sound produced at any given frequency and amplitude would be directly perceptible to the human ear is an additional question that is far from fully understood. Part of the high end audio experience is to capture sounds present in the original performance that we cannot hear, but because of how these inaudible signals interact with what we can hear, it affects our perception of fidelity. Spend time in a large concert hall with an orchestra or wind ensemble, one will be aware of very low frequency pressure changes in the hall that can not be directly heard, but affect how what is heard sounds. Bring in the percussion and low brass and it is obvious. Any reproduction system that cannot recreate these effects to some extent will not transport the listener to that hall. Such occurrences are the justification for extended frequency response above and below audible frequencies.
There is also an issue with indirect perception. Some examples of indirect perception are good, like the concert hall cited above, and some are not. Every loudspeaker ever made colors sound a little differently from every other loudspeaker and none of them produce the exact sound of the actual live music. This coloration comes from indirectly perceptible factors in the response of the loudspeaker. The problem here is that the more indirect the effect is, the harder it is to include in a mathematical reconstruction of human hearing.
Now throw in time delays from potential energy of the strain pushed into the cabinet and back out into the air at a slightly later time, and the question become harder to quantify. A stiffer cabinet will both reduce the amount of strain (i.e. less deformation) that absorbs energy and decreases the time delay because of the increase to the speed of wave propagation as this energy accordions into and out of the system.
To answer the original question is that potential audibility of cabinet resonances will be specific to a particular cabinet design, so there are no hard and fast rules, just good design practices that generally lead to good results, but not always. A particular cabinet geometry may need more or less bracing than a different cabinet design to be considered acceptable. But, when has merely being acceptable been acceptable to an audiophile?
In the end, a stiffer cabinet will produce a smaller amplitude of air movement and therefore less unwanted sound, regardless of if it is directly perceptible or not.
David
