Objection 1. It would seem that in the state of innocence men would not have been born in a state of righteousness. For Hugh of St. Victor says (De Sacram. i): "Before sin the first man would have begotten children sinless; but not heirs to their father's righteousness."
Objection 2. Further, righteousness is effected by grace, as the Apostle says (Romans 5:16-21). Now grace is not transfused from one to another, for thus it would be natural; but is infused by God alone. Therefore children would not have been born righteous.
Objection 3. Further, righteousness is in the soul. But the soul is not transmitted from the parent. Therefore neither would righteousness have been transmitted from parents, to the children.
On the contrary, Anselm says (De Concep. Virg. x): "As long as man did not sin, he would have begotten children endowed with righteousness together with the rational soul."
I answer that, Man naturally begets a specific likeness to himself. Hence whatever accidental qualities result from the nature of the species, must be alike in parent and child, unless nature fails in its operation, which would not have occurred in the state of innocence. But individual accidents do not necessarily exist alike in parent and child. Now original righteousness, in which the first man was created, was an accident pertaining to the nature of the species, not as caused by the principles of the species, but as a gift conferred by God on the entire human nature. This is clear from the fact that opposites are of the same genus; and original sin, which is opposed to original righteousness, is called the sin of nature, wherefore it is transmitted from the parent to the offspring; and for this reason also, the children would have been assimilated to their parents as regards original righteousness.
Reply to Objection 1. These words of Hugh are to be understood as referring, not to the habit of righteousness, but to the execution of the act thereof.
Reply to Objection 2. Some say that children would have been born, not with the righteousness of grace, which is the principle of merit, but with original righteousness. But since the root of original righteousness, which conferred righteousness on the first man when he was made, consists in the supernatural subjection of the reason to God, which subjection results from sanctifying grace, as above explained (95, 1), we must conclude that if children were born in original righteousness, they would also have been born in grace; thus we have said above that the first man was created in grace (95, 1). This grace, however, would not have been natural, for it would not have been transfused by virtue of the semen; but would have been conferred on man immediately on his receiving a rational soul. In the same way the rational soul, which is not transmitted by the parent, is infused by God as soon as the human body is apt to receive it.
From this the reply to the third objection is clear.
Source: Summa Theologica (New Advent)