Hm... good question. I wonder if not many of the 'pink' freshwater pearls would not fit in the range of color hues assigned to Pad sapphire to begin with: namely a warm pink-towards-orange rather then cold pink-towards-purple.
Some pinks are more orange than others and those seem to qualify even better, in theory... but wouldn't that be a silly! After all, sapphire is not the only gem that comes in that range of color, yet nothing else is called 'Padparadscha'.
That's a rather high pedestal to put anything on...
PS. not sure how common this is, but sometimes pearls are called
'cream-rose' to describe a mellow peach color, not unlike the color of said sapphires. I am definitely not saying that color alone is good reason to use the name,
definitely not (otherwise you'd have a bunch of topaz, spinel, tourmaline and even diamonds called 'pad' overnight just because they are light orange-pink in color - and what's the good of that?)