Still pretty implausible though. MANY newborn infants have heart murmurs -- my first son had one 25 years ago -- and the protocol at the time was "let it be, check it in six months, most of them heal on their own". It's far from being a major issue, generally speaking (and clearly wasn't, if Jo's wasn't 'corrected' until she was three), but I'd submit that the adoption-desperation for newborns, and especially a newborn with no presenting parents, would have been huge enough anyway that she'd have been adopted.
I think it was a miss by the writers. As, to some degree, from a different angle, was the Betty story. Placing an infant for adoption is all-too-rarely the mother's actual choice. Often it's deeply fraught. If anything, Jo's story with this set-up should have been an example of a best-possible scenario.