Something about the automatic changeover from civil to Sacrament sounds wrong to me. Where does the requirement for proper form, matter and intention fit in? Is the form the same in a civil marriage? Is the Catholic intention?
So, marriage is a bit different from the other Sacraments, but the validity depends upon expression of the contract for an indissoluble bond, and thus is the same for the natural equivalent and the Sacrament. But only Catholics can have the Sacraments, and so when contracted among non-Catholics it's not a Sacrament, but contracted among Catholics a Sacrament. But the essence (matter/form) is basically the same in both cases. From another perspective, Sacraments confer sanctifying grace, and non-Catholics cannot receive sanctifying grace.
Perhaps one analogy would be with the Sacrament of Baptism, though it's not perfect, where if you were to baptize someone who lacked the proper dispositions (let's say he doesn't really believe and isn't contrite, but just going through the motions for social reasons), the matter/form would be validly conferred, but no sanctifying grace would be transmitted. But if later the individual came to believe, had contrition for his sins, and went to Confession, the Sacrament would have its intended effects, putting the soul into a state of sanctifying grace ... and the matter/form would not be (and cannot be) repeated.