Even though I live out this way I've never used it. I have however used the shuttle from the AG Campus to TBA during basketball season and I've never had a problem. It's obviously a lot further from Farragut, but it's not bad. The only drawback is the looooooong line to stand in after the game.
I might recommend staying closer to the stadium (if you're not locked in) and driving in yourself. You can park for $10 at the Children's Hospital Employee parking garage and the money goes to a good cause. You do have a pretty long wait to get out after the game though, that's not always fun. It's also a bit of a hike.
Another place to park would be the office complex near the intersection of Neyland and Kingston Pike/Cumberland Ave. It's also $10, but it is SUPER easy to get out of and the walk isn't that much further than walking from the Children's Hospital location.
If you do take the shuttle, I'd be interested to know how you rate your experience. Also, nice avatar.