Nope, that is not what happened, that is not what the Bible says. Adam and Eve have sex for the first time in Genesis 4, which is after they are banished from Eden.
What happened in the Garden is that there was a tree called the tree of the knowledge of good and evil. God had given mankind authority over everything in the creation and told Adam and Eve that they could eat the fruit of any of the trees except for this tree and God forewarned them that in the day they ate of it that they would die.
You then have the dragon, an animal, and this is Satan. The dragon deceived the woman by telling her the first Three Lies, which is the first sin. Being deceived by the animal, their inferior whom they should have never listened to to begin with, the woman ate from the tree of the knowledge of good and evil. She then gave to Adam the fruit and he ate.
God then curses man to have to toil all the days of his life for disobeying God and throwing his God-given authority away to the world. God curses woman to have pain in childbirth and to serve her husband because she disobeyed and was deceived. Finally God curses the dragon above all the other animals because he is the father of the sins and the father of the lies and is the one ultimately responsible for all of this and he will never have any hope for redemption, but the Lord Jesus will return and utterly defeat Satan and slay him and throw him away forever into the burning lake of fire, amen.