My reading would say that as long as Mr. Palin was baptized using “The Father, The Son, and The Holy Spirit” it would be a valid marriage.
I think what is at issue is the status of the church performing the marriage (if the Palins were married in a church service rather than by a judge), regardless of Todd Palin’s baptism (I assume he was baptized). But they are saying the marriage is “prohibited” which isn’t quite the same as saying that it is invalid.
It would be invalid due to a defect in form.
Can. 1108 §1. Only those marriages are valid which are contracted before the local ordinary, pastor, or a priest or deacon delegated by either of them, who assist, and before two witnesses according to the rules expressed in the following canons and without prejudice to the exceptions mentioned in cann. ⇒ 144, ⇒ 1112, §1, ⇒ 1116, and ⇒ 1127, §§1-2.
Bottom line is that it would have to be convalidated, in the event that she wanted to come back to the Church. This, of course, assumes that Sarah did not receive a dispensation from her local pastor or ordinary, per Canon 1118.