In terms of canon law, no. But that kind of hair-splitting makes no logical sense to anyone except a canon lawyer, as Sheila Kennedy explained in Shattered Faith. Her book, by the way, had the very good effect of derailing at least one Kennedy's political career. Unfortunately, it did not seem to make a dent in the scandal of annulment-on-demand in the American Catholic Church. That will not end until we have a new and improved set of bishops. Sounds as if the guy in South Dakota might be pointing the way.
I'm 34 years old and I have never in my life seen anyone scandalised by the fact of legitimacy. Where we are now in this country illegitimacy is practically the norm, and for some populations it is.
Only a Kennedy would be distraught over such a thing.
SD
This problem came about as many others did in the "Spirit of Vatican II" push during the 70s. Priests started thinking in terms of 'compassion' and not in terms of taking people to task for their behavior. That has begun to change, and you'll see some folks leaving the Church because it has gotten too 'conservative', when the rules were always there, they just were not always enforced.
As far as the 'legitimacy of children' question goes, it helps to understand what an annulment is. It is not a statement that the couple was never legally married, that is a civil matter and one which determines legitimacy of the children. Annulment just says that the SACRAMENT was never valid, so if that wasn't valid, then that couple is able to marry in the Church as long as they are counselled to understand the meaning and seriousness of the Sacrament.