Can a parent with AB blood group have an O group child?

No it is not possible as the parent will transfer either Ia or Ib antigen to its progeny so whatever be the genotype of other parent the offspring can not have an O blood group( O blood group is recessive)

Since both parents have AB blood group their genotypes will beI^AI^B.On the other hand O blood group being a recessive trait, can be expressed when the genotype of the person is I^OI^O.But here the child cannot inherit I^O from either of the parents.So O blood group is not possible.