More check swing questions....

[Snorg]

A couple months ago we discussed this sitch (I will boil it down here to save digging)...
R1 stealing with two outs and two strikes, batter check swings, F2 retires runner, then the defense appeals the check swing, getting strike three, which erases the CS, and a new batter leads off the next inning. It was agreed that this could be beneficial to the defense if the batter were a heavy hitter.

My question is, can the offensive team appeal a check swing? Maybe the above sitch happens late in the game, with the batting team losing, and the #9 hitter at the plate. If R1 is retired, the defense is not going to (or at least shouldn't) appeal the check swing so the #9 man leads off the next inning. The offense, however, would like to appeal the swing, and have the top of the order lead off the next inning. (I admit that the coach would really have to be paying attention to do this, but I don't think this is a TWP).

In 9.02(b) and the note to 9.03 (c), the rule book refers only to 'the manager' or 'managers'. It does not denote offensive or defensive, unless you infer that 'The manager or the catcher...' in the note to 9.03(c) refers de facto to the defensive manager.

Any thoughts?