I don't have any info on the "studies" the other person is referring to. But I work in a neonatal intensive care unit, and I know from experience that some babies will shut down and withdraw when exposed to prolonged painful experiences, like when we have to do multiple pokes to get an IV in. I have no doubt that many babies who are circumcised without anesthesia may get to the place of shutting down, to attempt to cope with the pain, maybe something like going out of their bodies. Those that get an effective anesthesic block, however, may have enough blunting that they don't have to go into this withdrawal state, but may actually just be hanging out in a relatively relaxed looking state, just sucking away on their pacifier. So, yes, with anesthesia, some might just sleep through it.
Not that anesthesia is guaranteed to make it pain free. All the docs use dorsal penile nerve blocks at our hospital, and some of the babies are quiet the whole time, and some scream their heads off the whole time.
Not that anesthesia makes it right, in any case.
Gillian