I think there is a possibility that certain labor pains can be linked with infant survival. Usually one problem with epidurals is that they block all pain and women aren't signaled by their body as to when to push. I think the body signals through pain when something may be going wrong. However, because of today's technologies I don't believe it is as essential as it used to be.
Some have entertained the thought that labor pain is an evolutionary safeguard insuring the safety of an infant. Some people also believe that adrenaline released during labor pain is beneficial to the baby. Both of these arguments can be quickly be put aside simply by admitting that we live in a modern world where infants are not assaulted by wild beasts at the time of birth, and that a mother need not be alert and in pain to deliver a healthy baby. Ideas that labor pain is beneficial derive from both a reactionary religious view in which women deserve to suffer, and a newer, but just as irrational new age idea that anything natural is better.
I believe it is impossible to say if labor pain is important in infant survival. I can't really see a connection given that labor pain is supposedly forgotten quite quickly. I think we have valid ways to avoid this pain and I don't see a problem with using those options.
The general consensus on the cause of labor pain is that evolution favored walking upright and big brains more than comfortable labor. Walking about on two legs has worked out quite well for the species, but the trade-off has been a narrower birth canal. Having large brains has also been quite beneficial to the species, but the trade-off has been larger heads (even for babies). These two factors have combined to produce birth canals that are just barely (and some times not quite) large enough for the big heads that need to be passed through them. That is the cause of labor pain.