Scott,
the Tyros 2 has to my ears the best jazz guitar sound among all the arranger keyboards currently on the market. I own also a Fantom ES rack and a Motif XR and was unable to find a jazz guitar sound that comes close to the Tyros, not even on the Motif, and this goes to prove that they don't share the same sound set.
That said, I had a listen to the MP3 of Sweet Georgia Brown and, while I have to agree with others that a lot of the final result depends on the voicings used to play those chords, I think that it would be possible to work on the Tyros' Jazz Guitar and make it close to the sound you mentioned.
To do this, however, I am afraid that you would need a keyboard with greater sound editing possibilities, compared with the Tyros, because the following steps would be involved:
1- Close the hi-pass filter or, with a graphic equalizer, mute almost all the frequencies above 4000 Hz.
2- Mute all the low frequencies as well (let your ears be the judge here, but I would consider 500 Hz as a good cutoff point).
3- Boost the mid frequencies substantially (the amount depends on what kind of sound you are after; when I had a Gibson ES 175 and a Fender Super Reverb I used to set the mid level to "8", to get the Joe Pass sound... and I nailed it!)
4- On the Tyros 2 use one of the amp simulator effects, because this will add a lot of authenticity to your sound. The sound I hear on the MP3 is mono and no jazz guitar is good played in stereo (we are not talking Pat Metheny here!)
5- Keep the reverb level to the minimum and use one of the Room algorhythms (jazz guitars tend to sound bad in large halls and in fact you tipically hear them in a small environment, or at least that's the way they are supposed to sound...)

Let me know what you come up with...

[This message has been edited by Dreamer (edited 01-14-2008).]