Greek Orthodox Marriage Is Valid

A Catholic who marries in an Eastern Orthodox Church enters into a valid marriage, regardless of whether he was properly dispensed from canonical form (canon 1127 §1).

While the willingness to have children is essential to the validity of the sacrament, the willingness to raise children as Catholic is not essential to the validity of the sacrament.

Therefore, a Catholic who marries in a Greek Orthodox ceremony and has no intention of raising the children as Catholics does indeed enter into a valid marriage. There are, of course, serious spiritual questions that need to be addressed but not the validity of the marriage.