Even if Eve had not sinned, would she still have had some pain in childbirth, and would that apply to Mary?

First, we do not actually know that Christ's birth was painless; that is an assumption people make because Mary was sinless. The problem is that the figures used in Scripture, like the woman in Apocalypse 12 who cries out in the pain of delivery, and all the passages that compare God's coming judgment to a woman in travail, treat birth as painful. There is not a single passage, good, bad, or indifferent, that says birth is painless. Even Genesis 3:16, where God says he will increase her pain, implies the pain was already there in order to be increased. It only makes sense, because unless God intruded into the woman's nervous system, which we have no indication of, Adam and Eve had nerves like ours. Eve felt the ground under her feet, felt the fruit in her fingers, tasted it on her tongue and gums; all their anatomy worked as ours does. What was different was that they were protected. Today a person can fall off a cliff and God normally will not stop it, but in Eden that protection was the normal course of events, as Psalm 91 describes for the Son of Man: under God's protection every movement is guarded so no harm comes. Even so, when a woman bears a child something is a little abnormal, and God could allow a little pain as a reminder, but minimal. Eve's greater pain came because her whole aim in wanting to be a god was to escape childbearing, so God made the very thing she tried to avoid the place of her greater pain, which is the same disorder we see today in women who avoid children for the workforce.