The distinction strikes me as artificial. Marcel Mule taught at the Paris Conservatory, yet performed many premieres of important works for our instrument, and was recorded a fair amount. His successor, Deffayet, was the saxophonist for the Berlin Philharmonic (arguably, the highest-caliber "professional" ensemble in the world, certainly at that time), yet does his teaching at the Paris Conservatory (likely his most regular income stream) somehow diminish that achievement?
My experience, and what I personally strive for, is to achieve equal levels of professionalism and passion in both my teaching and performing. The limited "professional" performance opportunities available to saxophonists (as opposed to other orchestral instruments) mean that we, even more than others, must rely on a patchwork of classical performance, jazz performance, doubling gigs in pits, etc., in order to have a viable "professional" career. And, if we have a strong desire, ability, and passion, we may also marry a teaching career to our performing.
The notion that Hemke, Rousseau, Delangle, Mule, Deffayet, etc. are not "professional" saxophonists is an absurd one, as the original poster seems to imply that there has been but one "professional" saxophonist in history. Not much of a profession, if that is the case! I'm not sure what end would be served by such an exceedingly narrow definition of "professional." On the other end of the spectrum, plenty of musicians in a wide variety of genres who are marginally talented make a living in music, if our definition of professional merely relates to the financial aspect. By this definition, Britney Spears is a true professional, while Claude Delangle is not, as she makes (presumably) no income from teaching, while he does. An odd premise, don't you think?
For what it's worth, my dictionary's first definition of professionalism is "of, engaged in, or worthy of the high standards of, a profession." The third definition finally mentions income, "earning one's living from an activity, such as a sport, not normally thought of as an occupation." Webster's 2nd College Edition, 1980--and I doubt that the definition has changed much since then.