I don't think it'll be like that.
My thought was more that maybe their Pearls got swapped somehow.
White got the Pearl meant for Pink and Pink got the Pearl meant for White.
That could also explain why CG Pearl is so much better in every regard than other Pearls. She was made for the highest order.
But she wound up being given to Pink either by White herself or by some mistake, leaving Pink's intended Pearl to go to White who has clearly fucked up the poor thing.
If that's the case, I NEED a scene where Pearl is confronted by White Pearl and White Pearl fucking snaps at the idea that while she's had this torturous, painful existence the Pearl that was meant to be in her place was off losing her Diamond to MURDERCOCK.