Yes, and this reading has been around for ages. Here’s Philo:
The woman incurred the violent woes of travail-pangs, and the griefs which come one after another all through the remainder of life. Chief among them are all those that have to do with children at birth and in their bringing up, in sickness and in health, in good fortune and evil fortune.
– Philo, On the Account of the World’s Creation Given by Moses
Ian Provan is another current proponent of this reading:
The pain is not the pain of childbirth but the painful family circumstances (Heb. 'itsabon) in which the woman will now bring children into the world. In Genesis 3:17, the man is likewise told that he will now farm his land in the midst of pain (Heb. 'itsabon, NIV’s “painful toil”). The double use of 'itsabon in verses 16 and 17 emphasizes that the woman’s fate mirrors that of the man. Each will toil in painful circumstances, enduring not intermittent but ongoing pain. […]
The woman will experience family in the context of pain, for her relationship with her husband and their relationship with the earth is fractured. The kind of pain that children in such a dysfunctional world can cause will shortly be graphically illustrated in the story of Cain and Abel in Genesis 4.
– Ian Provan, Seriously Dangerous Religion, 117–19
To me, it seems like this reading fits a larger pattern in the Eden story where almost every detail is pregnant with greater meaning. It’s not an allegory – where details represent something else unrelated – but more of a pervasive metonymy where concrete word pictures of one aspect of something are used to call up the whole. A serpent who will eat dust speaks of humiliation and not merely diet. Humans who are “naked and unashamed” speaks of childlike innocence and not just a lack of clothing. The woman and man being made from the same flesh and bone speaks to their oneness and alikeness while Adam being from dust and destined for dust speaks to mortality.
This way of speaking is pervasive in the Bible. One easy example is the law about not muzzling the ox while it treads grain. Paul tells us flat out this cannot be limited to oxen but shows the need to pay workers. We’d still translate it using the word “ox,” but we shouldn’t read it as only meaning that.
Also, it is biblically common to use an early state to refer to the entire life (or even progeny). The battling seeds of serpent and woman don’t mean that the conflict happens before each “seed” is born. Prophets refer to Jacob to refer to currently-living Israelites. Likewise, it’s probably unwise to limit the painful conception of the woman to birth pains. That is the graphic example of the anguish in producing a family, just as thorns and thistles epitomize the struggle to produce food from the land. (Once this is seen, it also becomes clear that the woman and man’s judgements both apply to humans generally, not just each sex. This is already pretty obvious because not only men die, but both sexes are also involved in both raising a family and farming.)
I don’t think this reading can be pinned on literalists or overly zealous concordists. In what I’ve read it seems to come from those who read Genesis carefully as well-crafted literature and so are open to figures of speech that transcend the literal meaning.