I would say that the "peek a boo" game doesn't actually teach object permanence rather simply exploit it for amusement. There is a school of thought that believes that we are simply born with everything it takes to learn object permanence and as we grow older it sort of just occurs. Sort of like the idea of AMPA/NMDA receptor ratio increasing after a certain age in neurons that facilitate LTP and hence learning, we are perhaps simply neurologically incapable of object permanence because of lack of connection between certain group(s) of neurons and once it happens the child "learns" object permanence.

I personally really doubt, something as critical to our sanity as object permanence is going to be left up to nurturing. Think of the ramifications of a few neglected "cave infants" and how that would seriously affect the human race today.