I once wanted her to join, she's quite an interesting character imo, but I knew from the beginning that she was more of an arc princess than nakama material. I also wonder what 3-eyed tribe special powers are, it may even not be connected to reading poneglyphs, but maybe seeing the future or something like this. But yeah, even if Pudding somehow does end up on Sunny, she's likely to travel with the crew, but not be a SH, she's too weak and her DF isn't combat-oriented, so unless her dormant powers make her a Jean Gray kinda powerhouse, she will stay a princess
But it’s a backstory from the past, so it’s not like details matter.