Based on what? That she's willing to do Peter's share of the washing-up? There's a sharp division, as Ann's Patrol were astute enough to point out in Autumn Term, between Ann's self-sacrificing behaviour towards her family and her attitude towards the rest of the world, which is still principled but much more brisk and hard-headed. One might
almost call it Rowanish, in the small glimpses we see when she's dealing with her dormitory babies.

Also, Ann has no money. Therefore, short of Mme Orly leaving her an inheritance (and I'd say Ginty was a more likely beneficiary), I doubt Rivers would have been interested.