In my own experience, babies born shortly after admin of narcotics tend to be a little sluggish and can possibly have decreased respiratory effort (and potentially absent respiratory effort). These will potentially cause lower apgar scores. You can see the effects of narcotics to the baby on the monitor within minutes of administration in most cases. The heart rate becomes flat as variability decreases. That is why practitioners tend to not order narcotics if birth will likely occur in less than 3-4 hours. For example, many would give this to a first time pregnant mama who is 2cm, but refuse it to a 3rd time mama who is 5cm.
To be honest (and I'm not pro-epidural! ftr, I'm not "pro" anything except true choice) I've never seen any negative effects on a baby from an epidural OTHER THAN a "post epi-dip", which is where the mother's BP drops, causing the blood flow to baby to decrease, causing decelerations and/or fetal bradycardia. This can sometimes lead to a need for other medications (terbutaline, ephedrine, etc) or even a c-section depending on the length and severity. So it is a significant risk, but if mom and baby avoid that, I've yet to see any side effects such as poor tone, poor respiratory effort, lower apgars, etc.
For a c-section, spinal anesthesia is usually used as opposed to epidural anesthesia (unless there is already a functioning epidural in place). For c-sections performed under general anesthesia, the babies are again, sluggish with a poor effort. They may also be oxygen deprived if the mother was not successfully intubated immediately.
Babies born without the use of any pain medications, overall, seem to be slightly more alert and interested in the world around them.
