Jesse,
I have flown many, many sports charters at United. The team contracts out the whole airplane, they have specially selected Flight Attendants, personalized catering and we often pick them up and drop them off at a remote part of the airfield. These trips are typically part of the bid packet and are available to anybody who wants to bid them. I like flying them because we get to fly into different, sometimes smaller, airports than usual and it is just a nice break from the daily routine. I have never once spoken to an athlete though, United has a strict no autograph policy and quite frankly we are too busy to talk to anybody even if we had time.
I always enjoy the charter flights and the different challenges that they present.
Chris