Yes

Genesis 3:16 To the woman he said,
"I will greatly increase your pains in childbearing;
with pain you will give birth to children.
Your desire will be for your husband,
and he will rule over you."

Pain in childbirth is a consequence of the first sin.

2 Corinthians 12:7-9 To keep me from becoming conceited because of these surpassingly great revelations, there was given me a thorn in my flesh, a messenger of Satan, to torment me. Three times I pleaded with the Lord to take it away from me. But he said to me, "My grace is sufficient for you, for my power is made perfect in weakness." Therefore I will boast all the more gladly about my weaknesses, so that Christ's power may rest on me.

Paul and Job are both examples to me that God does let bad things happen to good people. God does not prevent all problems, and does not promise to make childbirth easy.

No

Galatians 3:13 Christ redeemed us from the curse of the law by becoming a curse for us, for it is written: "Cursed is everyone who is hung on a tree."

I have been redeemed. I am not under the curse and so do not have to suffer the consequences as they pertained to giving birth.

Matthew 9:22 Jesus turned and saw her. "Take heart, daughter," he said, "your faith has healed you." And the woman was healed from that moment.

Matthew 8:16 When evening came, many who were demon-possessed were brought to him, and he drove out the spirits with a word and healed all the sick.

Jesus did heal those who asked him. I have no reason to expect him to refuse to heal my body if I ask. I can have the easiest and safest childbirth possible by asking Jesus for it.