I cannot imagine a scenario where the PU would refuse to honor a check-swing appeal, for the outcome can only be favorable to him.
1. the BU says, "no swing," and your original judgement is validated.
-or-
2. the BU calls, "Strike!". You are one strike closer to beer-thirty, and any heat over the changed call is now on your partner.
It's a win-win, or at least a win-draw, from behind the plate.
No one asks for an appeal when the batter doesnt get the bat off his shoulder, so I still don't understand that aspect of the OP.
If some of the old salts here know of a scenario where the PU would NOT want to hear a check-swing appeal, I would appreciate hearing about it. Seriously. Maybe I'm missing something.