Not really, waist width is up to the designer. For example, Donek makes two 171s - both with an 11.2m sidecut, but one that is 18cm wide at the waist and one that is 19.5cm.
I suppose if you wanted to fix the nose and tail width at some arbitrary number, then yes, length, nose/tail width, and sidecut radius would determine waist width. However most designers fix the waist width at some number, and let the length and sidecut radius determine nose/tail width.
Burton seems to take a different approach - they seem to fix length, waist width, and sidecut <i>depth</i>, which results in a random sidecut radius number.