We cannot know what the Supreme Court would have ruled in the Poe case if it had actually ruled on the constitutionality of the Connecticut law. The Court chose not to rule on the law in that case. Instead, they dismissed the case on more technical grounds.
In order for the Supreme Court to consider a case on its merits, it must first find that someone has “standing” to sue. What this means is that someone must have actually been harmed by the law in question. In the Poe case, the Court ruled that Poe (a pseudonym) had not actually been harmed by the law. She was suing because she feared she might be prevented from getting birth control, not because it had actually been denied to her.
In the Griswold case, there was no such issue of standing. Estelle Griswold and Dr. C. Lee Buxton decided to open a birth control advice clinic after Poe. They wanted to see if the law was really dead and if no one could be harmed by it. When they did so, they were arrested. Once the two were arrested, they had standing to sue. The Supreme Court then had to rule on the constitutionality of the statute and decided to strike it down.
Thus, the statute emerged unscathed in Poe because of a technicality and was later overturned on its merits.