Hmmm... tough question Deacon!
But to appreciate jazz, my answer is NO. To appreciate it BETTER, my answer is: music theory alone is not enough.
A measure of an artists musical triumph is how an audience can relate to his output. The artist also chooses the crowd to attract, and allows his art to be subjected to their interpretation. Jazz, as with all music, chooses its means to convey emotions and to draw peoples emotions through its form. If an ordinary listener is moved by coltranes adventures, or kenny g's (sorry folks for using these two names in one sentence!) trips, then, the artist has succeeded. I've had a few friends (like the guys i introduced to you at the fete last year) who are great jazz fans. followers of davis, coltrane, monk, dexter gordon, etc, because they can relate to its emotional value. I did an experiment last night, as i was on the phone with my girlfriend, i snuck coltrane's "soultrane" album as backround music. my girlfriend isn't a musician, and her popular music tastes are very mainstream but not involved. I asked her- "how does this music make you feel? Can you describe how you find it?" she replied "Its old jazz, right? I've never listenend to this stuff before, but i find it very soothing, the whole atmosphere can affect you." Coltrane triumphs, over the BASIC emotional form. That perhaps, was Coltranes goal during that moment of creation.
Now, to appreciate it better is a whole different story. If you are a musician wanting to unravel the mystery of jazz, yes, theory will make you appreciate the artistic devices utilized in the art. But to appreciate it better, theory is not enough. The hardest question to ask is not HOW did he do it, but WHY. From "why", the theory becomes just another factor in the equation. History (the point of the music's creation) has to be looked at, be it the artists personal history or the social (dare I say, political) mood at that time. We cannot ignore this aspect, because doing so would be downplaying jazz's emotional significance. My non-musician friends have as leg-up over me, because they are so well versed in jazz's history and understood the struggles of the time, that the musical devices i knew made me feel quite... inadequate. Learning more (yet i know so little) of its roots and transitions helps you capture the moment much better, and gives theoretical devices a more solid ground for its utilization and existence, for the musician.
Musicians should better ears because we are expected to be conversant, even eloquent in our chosen artistic expression. it is mandatory for us to appreciate things better, but only to put these things to use for the audiences benefit.