Do Tony's stats factor in that a decent amount of his playing time has been alongside our terrible bench?
Yes the website I cited adjusts for the quality of your teammates. Adjusted +/- is still a very noisy measure though, so you really can't rely on it without tons, I mean years, worth of data.
But its a helpful tool, and confirms what your naked eye tells you about Tony. He hurts the team offensively with his lack of shooting and turnovers and helps the team by being a better athlete and defender at the 2/3.
What it does not adjust for is style of play. When TA is in the game with Rondo, they become a running team instead of a halfcourt team, and simply by filling a lane ahead of the ball TA makes Rondo much more effective-- even if TA never touches the ball.
Pierce doesn't fill lanes much any more. He just trails behind and looks for an open three.
TA would be really effective on a D'Antoni team that runs all the time.
No it doesn't care what the style of play, it cares about the results. The fast break you describe sounds nice, but what about the breaks that Tony gets where he turns it over or is fouled, (where he more often than anything will only make 1 free throw)
Meanwhile Pierce's trailing results in quality 3 points shots at times, and he's converting on 47% of his 3s! Other times, he doesn't contribute anything and the C's miss a chance.
In the end the team scores more points when Tony is off the court, because he's not a good offensive player. At least for our team.