We cannot be sure exactly what happened 7 centuries ago; we only have the one account. However something akin to this experiment did occur, albeit without the controlled conditions. In Romania during Communism thousands of children were consigned to orphanages where they were grossly neglected (warning: the linked article contains distressing details).
Many children died under this regime, but we can't tell how much was due to physical versus psychological factors. However many survived despite the neglect.
This article in the Guardian reports that the children have specific areas of the brain smaller than children with normal upbringing.
In conclusion, it seems that gross psychological neglect has measurable neurological consequences but is not generally fatal, contrary to the report of Salimbene di Adam.