The answer is yes. The best resource is Vance Dickason's Loudspeaker Design Cookbook, Section 5.40. Also, consider the papers written by:
J. K. Iverson, The Theory of Loudspeaker Cabinet Resonances, JAES, April 1973.
Juha Beckman, Effect of Panel Damping on Loudspeaker Enclosure Vibration, 101st AES Convention, November 1996.
You wrote, "The air resonates sympathetically and unless the cabinet can move in response (which will alter the results), the sound is considered to be 'colored'. I think that you meant to say that if the cabinet walls move or resonate it will color the sound.
I think that it is good practice to reduce cabinet resonances as much as reasonable. There becomes an asymptote where the amount of money and effort applied to squelching resonances does not provide a good return on investment. I suspect that point is pretty variable depending on the manufactures' and DIY goals and budgets.